Mercurial > forge
changeset 9892:8ad402be2313 octave-forge
main/quaternion --> extra/quaternion-legacy, extra/quaternion_oo --> main/quaternion
author | paramaniac |
---|---|
date | Wed, 28 Mar 2012 03:16:58 +0000 |
parents | d6803a233b2b |
children | 0ed233a0d08c |
files | extra/quaternion-legacy/COPYING extra/quaternion-legacy/DESCRIPTION extra/quaternion-legacy/doc/quaternion.ps extra/quaternion-legacy/inst/demoquat.m extra/quaternion-legacy/inst/qconj.m extra/quaternion-legacy/inst/qcoordinate_plot.m extra/quaternion-legacy/inst/qderiv.m extra/quaternion-legacy/inst/qderivmat.m extra/quaternion-legacy/inst/qinv.m extra/quaternion-legacy/inst/qmult.m extra/quaternion-legacy/inst/qtrans.m extra/quaternion-legacy/inst/qtransv.m extra/quaternion-legacy/inst/qtransvmat.m extra/quaternion-legacy/inst/quaternion.m extra/quaternion_oo/COPYING extra/quaternion_oo/DESCRIPTION extra/quaternion_oo/INDEX extra/quaternion_oo/Makefile extra/quaternion_oo/NEWS extra/quaternion_oo/devel/INFO extra/quaternion_oo/devel/PROJECTS extra/quaternion_oo/devel/RELEASE_PACKAGE extra/quaternion_oo/devel/RV9_Quaternions.txt extra/quaternion_oo/devel/Report_Basile_Graf.pdf extra/quaternion_oo/devel/demoml.m extra/quaternion_oo/devel/generate_quaternion_pdf.m extra/quaternion_oo/devel/makefile_quaternion.m extra/quaternion_oo/devel/pdfdoc/collect_texinfo_strings.m extra/quaternion_oo/devel/pdfdoc/info_generate_manual.txt extra/quaternion_oo/devel/pdfdoc/quaternion.tex extra/quaternion_oo/devel/q0.m extra/quaternion_oo/devel/q1.m extra/quaternion_oo/devel/q2.m extra/quaternion_oo/devel/q3.m extra/quaternion_oo/devel/q4.m extra/quaternion_oo/devel/q_2x2.m extra/quaternion_oo/devel/q_2x3.m extra/quaternion_oo/devel/qbug.m extra/quaternion_oo/devel/quat.pdf extra/quaternion_oo/devel/quaternion.ps extra/quaternion_oo/devel/quaternion_arrays.m extra/quaternion_oo/doc/quaternion.pdf extra/quaternion_oo/inst/@quaternion/abs.m extra/quaternion_oo/inst/@quaternion/blkdiag.m extra/quaternion_oo/inst/@quaternion/cat.m extra/quaternion_oo/inst/@quaternion/columns.m extra/quaternion_oo/inst/@quaternion/conj.m extra/quaternion_oo/inst/@quaternion/ctranspose.m extra/quaternion_oo/inst/@quaternion/diag.m extra/quaternion_oo/inst/@quaternion/diff.m extra/quaternion_oo/inst/@quaternion/display.m extra/quaternion_oo/inst/@quaternion/eq.m extra/quaternion_oo/inst/@quaternion/exp.m extra/quaternion_oo/inst/@quaternion/horzcat.m extra/quaternion_oo/inst/@quaternion/inv.m extra/quaternion_oo/inst/@quaternion/ispure.m extra/quaternion_oo/inst/@quaternion/ldivide.m extra/quaternion_oo/inst/@quaternion/log.m extra/quaternion_oo/inst/@quaternion/minus.m extra/quaternion_oo/inst/@quaternion/mldivide.m extra/quaternion_oo/inst/@quaternion/mpower.m extra/quaternion_oo/inst/@quaternion/mrdivide.m extra/quaternion_oo/inst/@quaternion/mtimes.m extra/quaternion_oo/inst/@quaternion/norm.m extra/quaternion_oo/inst/@quaternion/plus.m extra/quaternion_oo/inst/@quaternion/power.m extra/quaternion_oo/inst/@quaternion/private/norm2.m extra/quaternion_oo/inst/@quaternion/private/normv.m extra/quaternion_oo/inst/@quaternion/quaternion.m extra/quaternion_oo/inst/@quaternion/rdivide.m extra/quaternion_oo/inst/@quaternion/rows.m extra/quaternion_oo/inst/@quaternion/size.m extra/quaternion_oo/inst/@quaternion/subsasgn.m extra/quaternion_oo/inst/@quaternion/subsref.m extra/quaternion_oo/inst/@quaternion/times.m extra/quaternion_oo/inst/@quaternion/transpose.m extra/quaternion_oo/inst/@quaternion/uminus.m extra/quaternion_oo/inst/@quaternion/unit.m extra/quaternion_oo/inst/@quaternion/uplus.m extra/quaternion_oo/inst/@quaternion/vertcat.m extra/quaternion_oo/inst/q2rot.m extra/quaternion_oo/inst/qi.m extra/quaternion_oo/inst/qj.m extra/quaternion_oo/inst/qk.m extra/quaternion_oo/inst/rot2q.m extra/quaternion_oo/inst/test_quaternion.m extra/quaternion_oo/src/Makefile extra/quaternion_oo/src/is_real_array.cc main/quaternion/COPYING main/quaternion/DESCRIPTION main/quaternion/INDEX main/quaternion/Makefile main/quaternion/NEWS main/quaternion/devel/INFO main/quaternion/devel/PROJECTS main/quaternion/devel/RELEASE_PACKAGE main/quaternion/devel/RV9_Quaternions.txt main/quaternion/devel/Report_Basile_Graf.pdf main/quaternion/devel/demoml.m main/quaternion/devel/generate_quaternion_pdf.m main/quaternion/devel/makefile_quaternion.m main/quaternion/devel/pdfdoc/collect_texinfo_strings.m main/quaternion/devel/pdfdoc/info_generate_manual.txt main/quaternion/devel/pdfdoc/quaternion.tex main/quaternion/devel/q0.m main/quaternion/devel/q1.m main/quaternion/devel/q2.m main/quaternion/devel/q3.m main/quaternion/devel/q4.m main/quaternion/devel/q_2x2.m main/quaternion/devel/q_2x3.m main/quaternion/devel/qbug.m main/quaternion/devel/quat.pdf main/quaternion/devel/quaternion.ps main/quaternion/devel/quaternion_arrays.m main/quaternion/doc/quaternion.pdf main/quaternion/doc/quaternion.ps main/quaternion/inst/@quaternion/abs.m main/quaternion/inst/@quaternion/blkdiag.m main/quaternion/inst/@quaternion/cat.m main/quaternion/inst/@quaternion/columns.m main/quaternion/inst/@quaternion/conj.m main/quaternion/inst/@quaternion/ctranspose.m main/quaternion/inst/@quaternion/diag.m main/quaternion/inst/@quaternion/diff.m main/quaternion/inst/@quaternion/display.m main/quaternion/inst/@quaternion/eq.m main/quaternion/inst/@quaternion/exp.m main/quaternion/inst/@quaternion/horzcat.m main/quaternion/inst/@quaternion/inv.m main/quaternion/inst/@quaternion/ispure.m main/quaternion/inst/@quaternion/ldivide.m main/quaternion/inst/@quaternion/log.m main/quaternion/inst/@quaternion/minus.m main/quaternion/inst/@quaternion/mldivide.m main/quaternion/inst/@quaternion/mpower.m main/quaternion/inst/@quaternion/mrdivide.m main/quaternion/inst/@quaternion/mtimes.m main/quaternion/inst/@quaternion/norm.m main/quaternion/inst/@quaternion/plus.m main/quaternion/inst/@quaternion/power.m main/quaternion/inst/@quaternion/private/norm2.m main/quaternion/inst/@quaternion/private/normv.m main/quaternion/inst/@quaternion/quaternion.m main/quaternion/inst/@quaternion/rdivide.m main/quaternion/inst/@quaternion/rows.m main/quaternion/inst/@quaternion/size.m main/quaternion/inst/@quaternion/subsasgn.m main/quaternion/inst/@quaternion/subsref.m main/quaternion/inst/@quaternion/times.m main/quaternion/inst/@quaternion/transpose.m main/quaternion/inst/@quaternion/uminus.m main/quaternion/inst/@quaternion/unit.m main/quaternion/inst/@quaternion/uplus.m main/quaternion/inst/@quaternion/vertcat.m main/quaternion/inst/demoquat.m main/quaternion/inst/q2rot.m main/quaternion/inst/qconj.m main/quaternion/inst/qcoordinate_plot.m main/quaternion/inst/qderiv.m main/quaternion/inst/qderivmat.m main/quaternion/inst/qi.m main/quaternion/inst/qinv.m main/quaternion/inst/qj.m main/quaternion/inst/qk.m main/quaternion/inst/qmult.m main/quaternion/inst/qtrans.m main/quaternion/inst/qtransv.m main/quaternion/inst/qtransvmat.m main/quaternion/inst/quaternion.m main/quaternion/inst/rot2q.m main/quaternion/inst/test_quaternion.m main/quaternion/src/Makefile main/quaternion/src/is_real_array.cc |
diffstat | 173 files changed, 21821 insertions(+), 21821 deletions(-) [+] |
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Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +<http://www.gnu.org/licenses/>. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +<http://www.gnu.org/philosophy/why-not-lgpl.html>.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/DESCRIPTION Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,13 @@ +Name: quaternion +Version: 1.0.0 +Date: 2008-07-17 +Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +Maintainer: The Octave-Forge Community +Title: Quaternion Package +Description: Package for the manipulation of Quaternion's used for + frame transformation +Categories: Mathematics +Depends: octave (>= 3.1.0) +Autoload: yes +License: GPL version 3 or later +Url: http://octave.sf.net
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/doc/quaternion.ps Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,8786 @@ +%!PS (but not EPSF; comments have been disabled) +%DVIPSCommandLine: dvips tmp -o quaternion.ps +%DVIPSParameters: dpi=600, compressed, comments removed +%DVIPSSource: TeX output 1998.10.23:1515 +/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N +/X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 +mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} +ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale +isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div +hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul +TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} +forall round exch round exch]setmatrix}N /@landscape{/isls true N}B +/@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B +/FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{ +/nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N +string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N +end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{ +/sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0] +N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup +length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ +128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub +get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data +dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N +/rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup +/base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx +0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff +setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff +.1 sub]/id 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+5122 y Fi(h)895 5216 y Fo(I)g Fq(\(2)p Fo(q)1066 5179 +y Fk(2)1063 5239 y(4)1127 5216 y Fl(\000)20 b Fq(1\))h(+)f(2)7 +b(\026)-52 b Fo(q)10 b Fq(\026)-52 b Fo(q)1543 5179 y +Fh(T)1618 5216 y Fq(+)20 b(2\()7 b(\026)-52 b Fo(q)24 +b Fl(\002)c Fo(I)7 b Fq(\))p Fo(q)2068 5230 y Fk(4)2107 +5122 y Fi(i)2161 5216 y Fo(x)702 5384 y Fq(=)83 b(\(2)p +Fo(q)980 5347 y Fk(2)977 5407 y(4)1040 5384 y Fl(\000)20 +b Fq(1\))p Fo(x)h Fq(+)f(2)7 b(\026)-52 b Fo(q)10 b Fq(\026)-51 +b Fo(q)1509 5347 y Fh(T)1563 5384 y Fo(x)21 b Fq(+)f(2)p +Fo(q)1813 5398 y Fk(4)1852 5384 y Fq(\()7 b(\026)-52 +b Fo(q)23 b Fl(\002)d Fo(x)p Fq(\))p eop +8 7 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)g(Quaternions)f(\(In)m(tro)s +(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p Fo(:)p Fq(1)439 +b Fn(\(c\))32 b(1998)908 b Fq(8)0 399 y Fr(Remark)34 +b(1.4)46 b Fq(The)32 b(ab)s(o)m(v)m(e)i(deriv)-5 b(ation)31 +b(treats)i(a)f(quaternion)g(as)g(a)h(transformation)e(up)s(on)g(a)i(v)m +(ector)g(within)0 511 y(a)f(linear)d(space.)44 b(An)31 +b(alternativ)m(e)h(con)m(v)m(en)m(tion)g(is)f(used)f(in)g([R)-10 +b(W91)r(],)31 b(in)f(whic)m(h)g(the)i(quaternion)e(is)g(treated)j(as)0 +624 y(a)e(transformation)e(up)s(on)g(the)h(basis)g(v)m(ectors)h(of)g(a) +f(frame.)41 b(The)30 b(latter)g(con)m(v)m(en)m(tion)i(results)d(in)g(a) +i(sign)e(c)m(hange)0 737 y(of)i(the)f(angle)g(of)h(rotation,)g(i.e.,) +1150 941 y Fo(x)1202 955 y Fh(r)1323 941 y Fq(=)83 b(\(2)p +Fo(q)1601 904 y Fk(2)1598 964 y(4)1661 941 y Fl(\000)20 +b Fq(1\))p Fo(x)h Fq(+)f(2)7 b(\026)-52 b Fo(q)10 b Fq(\026)-52 +b Fo(q)2129 904 y Fh(T)2184 941 y Fo(x)20 b Fq(+)g(2)p +Fo(q)2433 955 y Fk(4)2472 941 y Fq(\()7 b(\026)-52 b +Fo(q)24 b Fl(\002)c Fo(x)p Fq(\))0 1146 y(Use)29 b(of)g(the)f(latter)h +(con)m(v)m(en)m(tion)h(results)d(in)g(a)i(similar)d(c)m(hange)k(in)d +(sign)h(in)f(the)i(time)f(deriv)-5 b(ativ)m(e)28 b(of)h(the)f(quater-)0 +1259 y(nion,)h(discussed)g(in)g(1.5.)0 1471 y Fr(M-\014le)46 +b Fj(qtransv)28 b Fq(Rotate)k(a)f(v)m(ector)227 1696 +y Fj(qtransv)46 b(is)h(the)g(function)f(defined)g(from:)g +(/home3/hodel/oct/quat/qt)o(rans)o(v.m)275 1922 y(vr)h(=)h +(qtransv\(vv,qr\))275 2035 y(rotate)e(a)i(3-vector)d(as)i(specified)f +(by)h(quaternion)e(qr)275 2148 y(q)i(=)h(\(ee,th\))93 +b(\(vector,)46 b(angle)g(notation\))275 2261 y(vr)h(=)h(\(vv)f(.)g +(ee\)*ee)f([projection)f(on)i(ee)g(unchanged)e(])514 +2374 y(+)i([vv)g(-)g(\(vv)g(.)h(ee\)*ee])e(cos\(th\))93 +b([what's)46 b(left)h(gets)f(scaled)g(by)i(cosine])514 +2487 y(+)f(\(vv)g(x)g(ee\))g(sin\(th\))571 b([and)47 +b(the)g(sine)f(term)h(completes)e(the)i(rotation])0 2711 +y Fr(M-\014le)f Fj(qtransvmat)57 b Fq(Obtain)30 b(3)20 +b Fl(\002)g Fq(3)31 b(rotation)g(matrix)e(from)h(a)h(quaternion)275 +2936 y Fj([xv,yv,zv])45 b(=)i(qtransvmat\(q\))275 3049 +y(xm)g(=)h(qtransvmat\(q\),)c(xm)j(=)g([xv)g(yv)g(zv])275 +3162 y(compute)f(x,y,z)g(axes)h(rotated)f(per)h(specified)e(quaternion) +g(q)0 3387 y Fr(Example)34 b(1.4)46 b Fq(Use)30 b(of)h(quaternions)e +(to)i(view)f(b)s(o)s(dy/inertial)d(frame)k(transformations:)0 +3575 y Fj(degrees)46 b(=)h(pi/180;)189 b(daz)47 b(=)h(30*degrees;)188 +b(del)46 b(=)i(-20*degrees;)0 3688 y(qazimuth)e(=)h +(quaternion\([0,0,1],daz\);)0 3801 y(qelevation)e(=)i +(quaternion\([cos\(daz\),sin\(d)o(az\),)o(0],)o(del\))o(;)0 +3914 y(qview)f(=)i(qmult\(qelevation,qazimut)o(h\);)0 +4139 y(th)f(=)h(0:5:20;)0 4252 y(ov)f(=)h(ones\(size\(th\)\);)0 +4365 y(myth)f(=)g([th,max\(th\)*ov)d(;)j(0*ov,th];)0 +4478 y(myth)g(=)g([[0:5:20])e(,)j(20*ones\(1,4\),20*ones\(1,4)o(\);)41 +b(...)382 4591 y(zeros\(1,5\),)k(5:5:20,)g(20*ones\(1,4\);)g(...)382 +4704 y(zeros\(1,5\),)g(zeros\(1,4\),)f([5:5:20]];)0 4930 +y(#)j(inertial)f(frame)g(quaternion)0 5043 y(qin)h(=)g(quaternion\([1)e +(0)i(0],180*degrees\);)0 5156 y(for)g(kk=1:length\(myth\(1,:\)\))95 +5269 y(figure\(kk\))95 5381 y(thy)g(=)h(myth\(1,kk\);)140 +b(thp)47 b(=)g(myth\(2,kk\);)141 b(thr)46 b(=)i(myth\(3,kk\);)p +eop +9 8 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)436 b Fn(\(c\))31 b(1998)902 b Fq(9)95 399 +y Fj(#)48 b(avoid)e(transformations)e(by)j(reversing)e(the)i(order)g +(of)g(multiplication!)95 511 y(qyi)g(=)h(quaternion\([0,0,1],thy*d)o +(egr)o(ees\))o(;)95 624 y(qp1)f(=)h(quaternion\([0,1,0],thp*d)o(egr)o +(ees\))o(;)95 737 y(qr2)f(=)h(quaternion\([1,0,0],thr*d)o(egr)o(ees\))o +(;)95 850 y(qbi)f(=)h(qmult\(qyi,qmult\(qp1,qr2\))o(\);)95 +1076 y(printf\("yaw=\0458.4f,)43 b(pitch=\0458.4f,)i(\\n)190 +b(qbi)47 b(=)g(\(\0458.4f\)i)f(+)h(\(\0458.4e\)j)f(+)h(\(\0458.4f\)k)f +(+)h(\()0 1189 y(\0458.4f\)\\n",thy,thp,)c(...)382 1302 +y(qbi\(1\),)j(qbi\(2\),)f(qbi\(3\),)h(qbi\(4\)\);)95 +1415 y([vv,th])g(=)i(quaternion\(qbi\);)95 1528 y(printf\(")285 +b(=)47 b(\(vector\))f(=)h([\0458.4f)f(\0458.4f)h(\0458.4f],)e +(th=\0455.2f)h(deg\\n",)g(...)382 1641 y(vv\(1\),)g(vv\(2\),)g +(vv\(3\),)g(th*180/pi\);)95 1866 y(#)i(transform)d(qbi)i(to)g +(reference)f(coordinates)95 1979 y(qb)i(=)f(qmult\(qin,qbi\);)95 +2092 y(title\(sprintf\("yaw=\0455.2f,)41 b(pitch=\0455.2f,)k +(roll=\0455.2f)g(\(deg\)",thy,thp,thr\)\))95 2205 y +(coordinate_plot\(qin,qb,qvi)o(ew\);)95 2318 y(gset)i(terminal)f +(postscript)f(eps)95 2431 y(eval\(sprintf\("gset)e(output)j +('fig\045d.eps'",kk\)\);)95 2544 y(replot)95 2657 y(gset)h(terminal)f +(x11)0 2770 y(endfor)0 2957 y Fq(Results:)316 2924 y +Fk(1)50 4816 y @beginspecial 50 @llx 50 @lly 410 @urx +302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 0.00 deg) Cshow +2737 4900 M +(reference coordinates) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +2252 2272 L +2737 2625 Pls +2252 2272 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +-177 970 V +2737 2625 Crs +2560 3595 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +2252 2272 L +2737 2625 Star +2252 2272 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +-177 970 V +2737 2625 Box +2560 3595 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-177 970 V +-89 0 V +1.000 UL +LT3 +3323 1302 M +-1789 0 V +1181 3242 L +970 706 V +1789 0 V +4293 2008 L +3323 1302 L +970 706 V +-1788 0 V +2151 3948 L +2505 2008 L +1534 1302 L +1.000 UL +LT4 +3940 3948 M +2969 3242 L +-1788 0 V +1788 0 V +3323 1302 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 0.00 deg) Cshow +2737 4900 M +(yaw= 0.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Pls +3369 3141 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +-73 0 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 0 4911 1560 4 v 104 4965 a Fe(1)138 4997 +y Fc(due)28 b(to)g(details)h(of)g(visualization)h(soft)n(w)n(are,)h +(the)d Fb(x)18 b Fa(\000)g Fb(y)j Fa(\000)e Fb(z)31 b +Fc(axes)d(do)g(not)g(app)r(ear)h(as)g(a)f(righ)n(t-handed)f(co)r +(ordinate)j(system.)0 5088 y(Sorry)-6 b(.)p eop +10 9 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(10)50 2045 +y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 +@rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 5.00 deg) Cshow +2737 4900 M +(yaw= 5.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3409 2580 M +-672 45 V +3409 2580 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +693 514 V +2737 2625 Pls +3430 3139 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +78 5 V +10 10 V +6 10 V +3 9 V +-3 7 V +-6 6 V +-10 3 V +-14 2 V +-16 -1 V +-18 -3 V +-20 -6 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 10.00 deg) Cshow +2737 4900 M +(yaw=10.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3346 2535 M +-609 90 V +3346 2535 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +749 508 V +2737 2625 Pls +3486 3133 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +83 9 V +8 11 V +5 9 V +0 8 V +-4 7 V +-8 5 V +-11 2 V +-15 1 V +-17 -2 V +-19 -4 V +-21 -6 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly +410 @urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 15.00 deg) Cshow +2737 4900 M +(yaw=15.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3279 2491 M +-542 134 V +3279 2491 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +800 499 V +2737 2625 Pls +3537 3124 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +87 14 V +7 10 V +2 9 V +-1 7 V +-6 6 V +-9 4 V +-13 2 V +-16 -1 V +-18 -3 V +-20 -5 V +-20 -6 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 20.00 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3207 2448 M +-470 177 V +3207 2448 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +90 18 V +5 10 V +1 8 V +-3 7 V +-7 5 V +-11 3 V +-14 1 V +-17 -2 V +-19 -3 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial eop +11 10 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(11)50 2045 +y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 +@rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 20.00 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3207 2448 M +-470 177 V +3207 2448 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +90 18 V +5 10 V +1 8 V +-3 7 V +-7 5 V +-11 3 V +-14 1 V +-17 -2 V +-19 -3 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 20.61 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch= 5.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3173 2527 M +-436 98 V +3173 2527 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +405 -906 V +2737 2625 Crs +3142 1719 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-375 886 V +90 18 V +5 10 V +1 9 V +-3 7 V +-7 5 V +-11 3 V +-15 1 V +-17 -1 V +-18 -4 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly +410 @urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 22.34 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch=10.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3136 2606 M +-399 19 V +3136 2606 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +441 -911 V +2737 2625 Crs +3178 1714 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-384 878 V +89 18 V +6 11 V +0 9 V +-3 7 V +-7 5 V +-11 3 V +-15 1 V +-16 -1 V +-19 -4 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 24.95 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch=15.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3096 2686 M +-359 -61 V +3096 2686 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +474 -909 V +2737 2625 Crs +3211 1716 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-394 870 V +90 18 V +5 11 V +1 9 V +-4 8 V +-7 5 V +-11 3 V +-14 1 V +-17 -1 V +-19 -4 V +-20 -6 V +-19 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial eop +12 11 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(12)50 2045 +y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 +@rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 28.21 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch=20.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3054 2765 M +2737 2625 L +3054 2765 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +504 -901 V +2737 2625 Crs +3241 1724 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-403 861 V +89 19 V +5 11 V +1 10 V +-3 7 V +-7 6 V +-11 3 V +-15 1 V +-16 -1 V +-19 -4 V +-20 -6 V +-19 -9 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 28.71 deg) Cshow +2737 4900 M +(yaw=20.00, pitch=20.00, roll=10.00 \(deg\)) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3622 3070 M +2737 2625 L +3622 3070 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +236 176 V +2737 2625 Pls +2973 2801 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +476 -915 V +2737 2625 Crs +3213 1710 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +485 353 V +2737 2625 Star +3222 2978 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +177 -970 V +2737 2625 Box +2914 1655 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-140 990 V +100 8 V +2 6 V +-2 5 V +-7 4 V +-11 3 V +-14 2 V +-18 1 V +-19 0 V +-21 -2 V +-22 -3 V +-21 -4 V +1.000 UL +LT3 +3323 1302 M +-1789 0 V +1181 3242 L +970 706 V +1789 0 V +4293 2008 L +3323 1302 L +970 706 V +-1788 0 V +2151 3948 L +2505 2008 L +1534 1302 L +1.000 UL +LT4 +3940 3948 M +2969 3242 L +-1788 0 V +1788 0 V +3323 1302 L +stroke +grestore +end +showpage + @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly +410 @urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 30.19 deg) Cshow +2737 4900 M +(yaw=20.00, pitch=20.00, roll=15.00 \(deg\)) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3622 3070 M +2737 2625 L +3622 3070 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +277 95 V +2737 2625 Pls +3014 2720 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +454 -927 V +2737 2625 Crs +3191 1698 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +485 353 V +2737 2625 Star +3222 2978 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +177 -970 V +2737 2625 Box +2914 1655 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-129 990 V +100 6 V +3 6 V +-2 5 V +-7 5 V +-10 3 V +-15 3 V +-17 1 V +-19 0 V +-21 -1 V +-22 -3 V +-21 -4 V +1.000 UL +LT3 +3323 1302 M +-1789 0 V +1181 3242 L +970 706 V +1789 0 V +4293 2008 L +3323 1302 L +970 706 V +-1788 0 V +2151 3948 L +2505 2008 L +1534 1302 L +1.000 UL +LT4 +3940 3948 M +2969 3242 L +-1788 0 V +1788 0 V +3323 1302 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V 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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/demoquat.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,259 @@ +## Copyright (C) 1998, 1999, 2000, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this pogram; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} demoquat () +## Demonstrate the functions available for manipulating quaternions. +## +## Thanks to Mr. Charles Hall, Dr. Don Krupp and Dr. Larry Mullins at +## NASA's Marshall Space Flight Center for notes and instruction in +## use and conventions with quaternions. - A. S. Hodel +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function opt = demoquat () + + opt = 0; + quitopt = 5; + + while (opt != quitopt) + opt = menu ("Quaternion function demo (c) 1998 A. S. Hodel, a.s.hodel@eng.auburn.edu", + "quaternion construction/data extraction", + "simple quaternion functions", + "transformation functions", + "body-inertial frame demo", + "Quit"); + + switch(opt) + + case(1) + printf("Quaternion construction/data extraction\n"); + help quaternion + prompt + cmd = "q = quaternion(1,2,3,4)"; + run_cmd + disp("This format stores the i,j,k parts of the quaternion first;") + disp("the real part is stored last.") + prompt + disp(" ") + disp("i, j, and k are all square roots of -1; however they do not") + disp("commute under multiplication (discussed further with the function") + disp("qmult). Therefore quaternions do not commute under multiplcation:") + disp(" q1*q2 != q2*q1 (usually)") + prompt + + disp("Quaternions as rotations: unit quaternion to represent") + disp("rotation of 45 degrees about the vector [1 1 1]") + cmd = "degrees = pi/180; q1 = quaternion([1 1 1],45*degrees)"; + run_cmd + prompt + cmd = "real_q = cos(45*degrees/2)"; + run_cmd + printf("The real part of the quaternion q(4) is cos(theta/2).\n----\n\n"); + cmd = "imag_q = sin(45*degrees/2)*[1 1 1]/norm([1 1 1])" + run_cmd + disp("The imaginary part of the quaternion is sin(theta/2)*unit vector"); + disp("The constructed quaternion is a unit quaternion."); + prompt + disp("Can also extract both forms of the quaternion:") + disp("Vector/angle form of 1i + 2j + 3k + 4:") + cmd = "[vv,th] = quaternion(q)"; + run_cmd + cmd = "vv_norm = norm(vv)"; + run_cmd + disp("Returns the eigenaxis as a 3-d unit vector"); + disp("Check values: ") + cmd = "th_deg = th*180/pi"; + run_cmd + disp("") + disp("This concludes the quaternion construction/extraction demo."); + prompt + + case(2) + printf("Simple quaternion functions\n"); + cmd = "help qconj"; + run_cmd + cmd = "degrees = pi/180; q1 = quaternion([1 1 1],45*degrees)"; + run_cmd + cmd = "q2 = qconj(q1)"; + run_cmd + disp("The conjugate changes the sign of the complex part of the") + printf("quaternion.\n\n"); + prompt + printf("\n\n\nMultiplication of quaternions:\n"); + cmd = "help qmult"; + run_cmd + cmd = "help qinv" + run_cmd + disp("Inverse quaternion: q*qi = qi*q = 1:") + cmd = "q1i = qinv(q1)"; + run_cmd + cmd = "one = qmult(q1,q1i)"; + run_cmd + + printf("Conclusion of simple quaternion functions"); + prompt + + case(3) + printf("Transformation functions\n"); + disp("A problem with the discussion of coordinate transformations is that"); + disp("one must be clear on what is being transformed: does a rotation of"); + disp("theta degrees mean that you're rotating the VECTOR by theta degrees,"); + disp("also called the 'active convention,' or does it mean that you rotate "); + disp("the COORDINATE FRAME by theta degrees, also called the 'passive convention,' "); + disp("which is equivalent to rotating the VECTOR by (-theta) degrees. The"); + disp("functions in this demo use the active convention. I'll point out where"); + disp("this changes the code as the demo runs."); + disp(" -- The author"); + prompt + printf("\n\n"); + disp("Sequences of rotations:") + printf("\n\nRotation of a vector by 90 degrees about the reference z axis\n"); + cmd = "qz = quaternion([0 0 1], pi/2);"; + disp(cmd) ; eval(cmd); + printf("\n\nRotation of a vector by 90 degrees about the reference y axis\n"); + cmd="qy = quaternion([0 1 0], pi/2);"; + disp(cmd) ; eval(cmd); + printf("\n\nRotation of a vector by 90 degrees about the reference x axis\n"); + cmd="qx = quaternion([1 0 0], pi/2);"; + run_cmd + printf("\n\nSequence of three rotations: 90 degrees about x, then 90 degrees\n"); + disp("about y, then 90 degrees about z (all axes specified in the reference frame):"); + qchk = qmult(qz,qmult(qy,qx)); + cmd = "[vv,th] = quaternion(qchk), th_deg = th*180/pi"; + run_cmd + disp("The sequence of the three rotations above is equivalent to a single rotation") + disp("of 90 degrees about the y axis. Check:"); + cmd = "err = norm(qchk - qy)"; + run_cmd + + disp("Transformation of a quaternion by a quaternion:") + disp("The three quaternions above were rotations specified about") + disp("a single reference frame. It is often convenient to specify the"); + disp("eigenaxis of a rotation in a different frame (e.g., when computing"); + disp("the transformation rotation in terms of the Euler angles yaw-pitch-roll)."); + cmd = "help qtrans"; + run_cmd + disp("") + disp("NOTE: If the passive convention is used, then the above"); + disp("formula changes to v = qinv(q)*v*q instead of ") + disp("v = q*v*qinv(q).") + prompt + disp("") + disp("Example: Vectors in Frame 2 are obtained by rotating them from ") + disp(" from Frame 1 by 90 degrees about the x axis (quaternion qx)") + disp(" A quaternion in Frame 2 rotates a vector by 90 degrees about") + disp(" the Frame 2 y axis (quaternion qy). The equivalent rotation") + disp(" in the reference frame is:") + cmd = "q_eq = qtrans(qy,qx); [vv,th] = quaternion(q_eq)"; + run_cmd + disp("The rotation is equivalent to rotating about the reference z axis") + disp("by 90 degrees (quaternion qz)") + prompt + + disp("Transformation of a vector by a quaternion"); + cmd = "help qtransv"; + run_cmd + + disp("NOTE: the above formula changes if the passive quaternion ") + disp("is used; the cross product term is subtracted instead of added."); + prompt + disp("Example: rotate the vector [1,1,1] by 90 degrees about the y axis"); + cmd = "vec_r = qtransv([1,1,1],qy)"; + run_cmd + prompt + disp("Equivalently, one may multiply by qtransvmat:") + cmd = "help qtransvmat"; + run_cmd + disp("NOTE: the passive quaternion convention would use the transpose") + disp("(inverse) of the orthogonal matrix returned by qtransvmat."); + prompt + cmd = "vec_r_2 = qtransvmat(qy)*[1;1;1]; vec_err = norm(vec_r - vec_r_2)"; + run_cmd + + disp("") + disp("The last transformation function is the derivative of a quaternion") + disp("Given rotation rates about the reference x, y, and z axes."); + cmd = "help qderivmat"; + run_cmd + disp("") + disp("Example:") + disp("Frame is rotating about the z axis at 1 rad/s") + cmd = "Omega = [0,0,1]; Dmat = qderivmat(Omega)"; + run_cmd + disp("Notice that Dmat is skew symmetric, as it should be.") + disp("expm(Dmat*t) is orthogonal, so that unit quaternions remain") + disp("unit quaternions as the rotating frame precesses."); + disp(" ") + disp("This concludes the transformation demo."); + prompt; + + case(4) + printf("Body-inertial frame demo: Look at the source code for\n"); + printf("demoquat.m and qcoordinate_plot.m to see how it's done.\n"); + + # i,j,k units + iv = quaternion(1,0,0,0); jv = quaternion(0,1,0,0); + kv = quaternion(0,0,1,0); + + # construct quaternion to desired view. + degrees = pi/180; daz = 45*degrees; del = -30*degrees; + qazimuth = quaternion([0,0,1],daz); + qelevation = quaternion([cos(daz),sin(daz),0],del); + qview = qmult(qelevation,qazimuth); + + # inertial frame i, j, k axes. + iif = iv; jf = qtrans(jv,iv); kf = qtrans(kv,iv); + + # rotation steps + th = 0:5:20; ov = ones(size(th)); myth = [th,max(th)*ov ; 0*ov,th]; + + # construct yaw-pitch-roll cartoon + for kk=1:length(myth(1,:)) + thy = myth(1,kk); + thp = myth(2,kk); + + qyaw = quaternion([0,0,1],thy*pi/180); + [jvy,th] = quaternion(qtrans(jf,qyaw)); + qpitch = quaternion(jvy(1:3),thp*pi/180); + qb = qmult(qpitch, qyaw); + qi = quaternion([1, 0, 0],180*degrees); + + printf("yaw=%8.4f, pitch=%8.4f, \n qbi = (%8.4f)i + (%8.4e)j + (%8.4f)k + (%8.4f)\n",thy,thp, ... + qb(1), qb(2), qb(3), qb(4)); + [vv,th] = quaternion(qb); + printf(" = (vector) = [%8.4f %8.4f %8.4f], th=%5.2f deg\n", ... + vv(1), vv(2), vv(3), th*180/pi); + fflush (stdout); + qb = qmult(qb,qi); + title(sprintf("yaw=%5.2f deg, pitch=%5.2f deg",thy,thp)) + qcoordinate_plot(qi,qb,qview); + drawnow (); + endfor + + case(quitopt) + printf ("Exiting quaternion demo\n"); + + otherwise + error ("invalid option %f", opt); + + endswitch + endwhile + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qconj.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,42 @@ +## Copyright (C) 1998, 2000, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qconj (@var{q}) +## Conjugate of a quaternion. +## +## @example +## q = [w, x, y, z] = w*i + x*j + y*k + z +## qconj (q) = -w*i -x*j -y*k + z +## @end example +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function retval = qconj (q) + + if (nargin != 1 ) + print_usage (); + endif + + [a, b, c, d] = quaternion (q); + + retval = quaternion (-a, -b, -c, d); + +endfunction +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qcoordinate_plot.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,131 @@ +## Copyright (C) 1998, 1999, 2000, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qcoordinate_plot (@var{qf}, @var{qb}, @var{qv}) +## Plot in the current figure a set of coordinate axes as viewed from +## the orientation specified by quaternion @var{qv}. Inertial axes are +## also plotted: +## +## @table @var +## @item qf +## Quaternion from reference (x,y,z) to inertial. +## @item qb +## Quaternion from reference to body. +## @item qv +## Quaternion from reference to view angle. +## @end table +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function qcoordinate_plot (qf, qb, qv) + + if (nargin != 3 ) + print_usage (); + endif + + degrees = pi / 180; + d180 = 180 * degrees; + + ## construct coordinate transformation to view frame + + cm = qtransvmat(qv); + + p1 = [-1, -1, 1]; + p2 = [-1, -1, -1]; + p3 = [ 1, -1, -1]; + p4 = [ 1, -1, 1]; + p5 = [-1, 1, 1]; + p6 = [ 1, 1, 1]; + p7 = [ 1, 1, -1]; + p8 = [-1, 1, -1]; + + ## outline positive quadrant + + box1 = cm * [p4; p6; p5; p6; p7]'; + + ## outline rest of the box + + box2 = cm * [p7; p8; p5; p1; p4; p3; p7; p3; p2; p1; p2; p8]'; + + ## compute inertial to body rotation eigenaxis + ## qb = qbf*qf => qbf = qb/qf + ## + ## need to use inverse quaternion to rotate axes + + qbf = qinv (qmult (qb, qinv (qf))); + + [eaxv, th_eig] = quaternion (qbf); + + ## draw 1/3 circle in x-y plane around a unit z axis + + th = (0:-12:-120) * degrees * sign (th_eig); + lth = length (th); + + cpts = [0, 0, 0.1*cos(th); + 0, 0, 0.1*sin(th); + 0, 1, 1*ones(1,lth)]; + + ## rotate the 1/3 circle around eigenaxis of inertial to body rotation + ## qez = qe/qz = rotation to get from z axis to eigenaxis. + ## This rotates the 1/3 circle from x-y plane to the plane normal to + ## eigenaxis + + qez = qmult (qbf, qinv (quaternion (0, 0, 1, 0))); + eig_xm = qtransvmat (qez); + cpts = cm*eig_xm * cpts; + + ## transform inertial and body quaternions to view coordinates (rotate + ## by azimuth, elevation) + + qfm = qtransvmat (qf); + qbm = qtransvmat (qf); + + qf = qmult (qv, qf); + qb = qmult (qv, qb); + + ## get coordinate axes in inertial and reference frame + + jnk = qtransvmat (qf); + ifv = jnk(:,1); + jfv = jnk(:,2); + kfv = jnk(:,3); + + jnk = qtransvmat (qb); + ibv = jnk(:,1); + jbv = jnk(:,2); + kbv = jnk(:,3); + + axis ([-2, 2, -2, 2], "square"); + + [vv, theta] = quaternion (qb); + + xlabel (sprintf ("rotate about eigenaxis %5.2f deg", th_eig/degrees)); + + plot ([ibv(1), 0], [ibv(3), 0], "-@11;x (body);", + [0, jbv(1)], [0, jbv(3)], "-@21;y (body);", + [0, kbv(1)], [0, kbv(3)], "-@32;z (body);", + [ifv(1), 0], [ifv(3), 0], "-@13;x (inertial);", + [0, jfv(1)], [0, jfv(3)], "-@23;y (inertial);", + [0, kfv(1)], [0, kfv(3)], "-@34;z (inertial);", + cpts(1,:), cpts(3,:), ".-6 ;eigenaxis;", + box2(1,:), box2(3,:), "-4;;", + box1(1,:), box1(3,:), "-5;;"); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qderiv.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,58 @@ +## Copyright (C) 1998, 2000, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qderiv (omega) +## Derivative of a quaternion. +## +## Let Q be a quaternion to transform a vector from a fixed frame to +## a rotating frame. If the rotating frame is rotating about the +## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative +## of Q is given by +## +## @example +## Q' = qderivmat (omega) * Q +## @end example +## +## If the passive convention is used (rotate the frame, not the vector), +## then +## +## @example +## Q' = -qderivmat (omega) * Q +## @end example +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function Dmat = qderivmat (Omega) + + if (nargin != 1) + print_usage (); + endif + + Omega = vec (Omega); + + if (length (Omega) != 3) + error ("qderivmat: Omega must be a length 3 vector"); + endif + + Dmat = 0.5 * [ 0.0, Omega(3), -Omega(2), Omega(1); + -Omega(3), 0.0, Omega(1), Omega(2); + Omega(2), -Omega(1), 0.0, Omega(3); + -Omega(1), -Omega(2), -Omega(3), 0.0 ]; +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qderivmat.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,58 @@ +## Copyright (C) 1998, 2000, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qderivmat (@var{omega}) +## Derivative of a quaternion. +## +## Let Q be a quaternion to transform a vector from a fixed frame to +## a rotating frame. If the rotating frame is rotating about the +## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative +## of Q is given by +## +## @example +## Q' = qderivmat (omega) * Q +## @end example +## +## If the passive convention is used (rotate the frame, not the vector), +## then +## +## @example +## Q' = -qderivmat (omega) * Q. +## @end example +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function Dmat = qderivmat (Omega) + + if (nargin != 1 ) + print_usage (); + endif + + Omega = vec (Omega); + + if (length (Omega) != 3) + error ("qderivmat: Omega must be a length 3 vector"); + endif + + Dmat = 0.5 * [ 0.0, Omega(3), -Omega(2), Omega(1); + -Omega(3), 0.0, Omega(1), Omega(2); + Omega(2), -Omega(1), 0.0, Omega(3); + -Omega(1), -Omega(2), -Omega(3), 0.0 ]; +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qinv.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,43 @@ +## Copyright (C) 1998, 2000, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qinv (@var{q}) +## Return the inverse of a quaternion. +## +## @example +## q = [w, x, y, z] = w*i + x*j + y*k + z +## qmult (q, qinv (q)) = 1 = [0 0 0 1] +## @end example +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function retval = qinv (q) + + if (nargin != 1) + print_usage (); + endif + + if (norm (q) != 0) + retval = qconj (q) / sum (q .* q); + else + error ("qinv: zero quaternion passed!"); + endif + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qmult.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,57 @@ +## Copyright (C) 1998, 2000, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qmult (@var{a}, @var{b}) +## Multiply two quaternions. +## +## @example +## [w, x, y, z] = w*i + x*j + y*k + z +## @end example +## +## @noindent +## identities: +## +## @example +## i^2 = j^2 = k^2 = -1 +## ij = k jk = i +## ki = j kj = -i +## ji = -k ik = -j +## @end example +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function retval = qmult (a, b) + + if (nargin != 2 ) + print_usage (); + endif + + [a1, b1, c1, d1] = quaternion (a); + [a2, b2, c2, d2] = quaternion (b); + + ri = b1*c2 - c1*b2 + d1*a2 + a1*d2; + rj = c1*a2 - a1*c2 + d1*b2 + b1*d2; + rk = a1*b2 - b1*a2 + d1*c2 + c1*d2; + rr = -(a1*a2 + b1*b2 + c1*c2) + d1*d2; + + retval = quaternion (ri, rj, rk, rr); + +endfunction +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qtrans.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,41 @@ +## Copyright (C) 1998, 2000, 2002, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qtrans (@var{v}, @var{q}) +## Transform the unit quaternion @var{v} by the unit quaternion @var{q}. +## Returns @code{@var{v} = @var{q}*@var{v}/@var{q}}. +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function v = qtrans (v, q) + + if (nargin != 2) + print_usage (); + endif + + if (! isvector (v) || length (v) != 4) + error ("qtrans: v(%d,%d) must be a quaternion", rows (v), columns (v)); + elseif (! isvector (q) || length (q) != 4) + error ("qtrans: q(%d,%d) must be a quaternion", rows (q), columns (q)); + endif + + v = qmult (q, qmult (v, qinv (q))); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qtransv.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,50 @@ +## Copyright (C) 1998, 2000, 2002, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qtransv (@var{v}, @var{q}) +## Transform the 3-D vector @var{v} by the unit quaternion @var{q}. +## Return a column vector. +## +## @example +## vi = (2*real(q)^2 - 1)*vb + 2*imag(q)*(imag(q)'*vb) +## + 2*real(q)*cross(imag(q),vb) +## @end example +## +## @noindent +## Where imag(q) is a column vector of length 3. +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function vi = qtransv (vb, qib) + + if (! isvector (vb) || length (vb) != 3) + error ("qtransv: v(%d,%d) must be a 3-D vector", rows (vb), columns (vb)); + elseif (! isvector (qib) || length (qib) != 4) + error ("qtransv: q(%d,%d) must be a quaternion", rows (qib), columns (qib)); + elseif (max (abs (imag (vb))) + max (abs (imag (qib))) != 0) + error ("qtransv: input values must be real"); + endif + + qr = qib(4); + qimag = vec (qib(1:3)); + vb = vec (vb); + vi = (2*qr^2 - 1)*vb + 2*qimag*(qimag'*vb) + 2*qr*cross (qimag, vb); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/qtransvmat.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,52 @@ +## Copyright (C) 1998, 2000, 2002, 2004, 2005, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {} qtransvmat (@var{qib}) +## Construct a 3x3 transformation matrix from quaternion @var{qib} that +## is equivalent to rotation of th radians about axis @var{vv}, where +## @code{[@var{vv}, @var{th}] = quaternion (@var{qib})}. +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function Aib = qtransvmat (qib) + + if (nargin != 1) + print_usage (); + endif + + if (! isvector(qib) || length (qib) != 4) + error ("qtransvmat: q(%d,%d) must be a quaternion", rows (qib), \ + columns (qib)); + elseif (max (abs (imag (qib))) != 0) + error ("qtransvmat: input values must be real"); + endif + + + Aib = [(2.*(qib(1)^2 + qib(4)^2) -1.), ... + (2.*(qib(1)*qib(2)-qib(3)*qib(4))), ... + (2.*(qib(1)*qib(3)+qib(2)*qib(4))); + (2.*(qib(1)*qib(2)+qib(3)*qib(4))), ... + (2.*(qib(2)*qib(2)+qib(4)*qib(4))-1.), ... + (2.*(qib(2)*qib(3)-qib(1)*qib(4))); + (2.*(qib(1)*qib(3)-qib(2)*qib(4))), ... + (2.*(qib(2)*qib(3)+qib(1)*qib(4))), ... + (2.*(qib(3)*qib(3)+qib(4)*qib(4))-1.)]; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/quaternion-legacy/inst/quaternion.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,114 @@ +## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 +## Auburn University. All rights reserved. +## +## This program is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## This program is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}] =} quaternion (w) +## @deftypefnx {Function File} {[@var{vv}, @var{theta}] =} quaternion (w) +## @deftypefnx {Function File} {@var{w} =} quaternion (@var{a}, @var{b}, @var{c}, @var{d}) +## @deftypefnx {Function File} {@var{w} =} quaternion (@var{vv}, @var{theta}) +## Construct or extract a quaternion +## +## @example +## w = a*i + b*j + c*k + d +## @end example +## +## @noindent +## from given data. +## @end deftypefn + +## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Adapted-By: jwe + +function [a, b, c, d] = quaternion (w, x, y, z) + + switch (nargin) + case(1) + if (! (isvector (w) && length (w) == 4)) + error ("input vector must be of length 4)"); + endif + ## extract data + switch (nargout) + case(4) + a = w(1); + b = w(2); + c = w(3); + d = w(4); + + case(2) + if (abs (norm (w) - 1) > 1e-12) + warning ("quaternion: ||w||=%e, setting=1 for vv, theta", norm(w)); + w = w/norm(w); + endif + [a, b, c, d] = quaternion (w); + theta = acos (d) * 2; + if (abs (theta) > pi) + theta = theta - sign (theta) * pi; + endif + sin_th_2 = norm ([a, b, c]); + + if (sin_th_2 != 0) + vv = [a, b, c] / sin_th_2; + else + vv = [a, b, c]; + endif + a = vv; + b = theta; + otherwise + print_usage (); + endswitch + + case(2) + if (nargout > 1) + print_usage (); + endif + vv = w; + theta = x; + + if (! isvector (vv) || length (vv) != 3) + error ("vv must be a length three vector"); + elseif (! isscalar (theta)) + error ("theta must be a scalar"); + elseif (norm (vv) == 0) + error ("quaternion: vv is zero"); + elseif (abs (norm (vv) - 1) > 1e-12) + warning ("quaternion: ||vv|| != 1, normalizing") + vv = vv / norm (vv); + endif + + if (abs (theta) > 2*pi) + warning ("quaternion: |theta| > 2 pi, normalizing") + theta = rem (theta, 2*pi); + endif + vv = vv * sin (theta / 2); + d = cos (theta / 2); + a = quaternion (vv(1), vv(2), vv(3), d); + + case(4) + if (nargout > 1) + print_usage (); + endif + if (! (isscalar (w) && isscalar (x) && isscalar (y) && isscalar (z))) + error ("input values must be scalars"); + endif + a = [w, x, y, z]; + + otherwise + print_usage (); + + endswitch + +endfunction
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--- a/extra/quaternion_oo/DESCRIPTION Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,11 +0,0 @@ -Name: quaternion -Version: 2.0.0 -Date: 2012-03-28 -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Maintainer: Lukas Reichlin <lukas.reichlin@gmail.com> -Title: Quaternion -Description: Overloaded operators for quaternions -Depends: octave (>= 3.6.0) -Autoload: yes -License: GPL version 3 or later -Url: http://octave.sf.net
--- a/extra/quaternion_oo/INDEX Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,44 +0,0 @@ -quaternion >> Quaternion -Quaternions - quaternion - qi - qj - qk - q2rot - rot2q -Methods - @quaternion/abs - @quaternion/blkdiag - @quaternion/cat - @quaternion/columns - @quaternion/conj - @quaternion/diag - @quaternion/diff - @quaternion/exp - @quaternion/inv - @quaternion/ispure - @quaternion/log - @quaternion/norm - @quaternion/rows - @quaternion/size - @quaternion/unit -Overloaded Operators - @quaternion/ctranspose - @quaternion/eq - @quaternion/horzcat - @quaternion/ldivide - @quaternion/minus - @quaternion/mldivide - @quaternion/mpower - @quaternion/mrdivide - @quaternion/mtimes - @quaternion/plus - @quaternion/power - @quaternion/rdivide - @quaternion/subsasgn - @quaternion/subsref - @quaternion/times - @quaternion/transpose - @quaternion/uminus - @quaternion/uplus - @quaternion/vertcat
--- a/extra/quaternion_oo/Makefile Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -sinclude ../../Makeconf - -PKG_FILES = COPYING DESCRIPTION INDEX NEWS $(wildcard inst/*) -SUBDIRS = doc/ - -.PHONY: $(SUBDIRS) - -pre-pkg:: - @for _dir in $(SUBDIRS); do \ - $(MAKE) -C $$_dir all; \ - done - -clean: - @for _dir in $(SUBDIRS); do \ - $(MAKE) -C $$_dir $(MAKECMDGOALS); \ - done
--- a/extra/quaternion_oo/NEWS Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,14 +0,0 @@ -Summary of important user-visible changes for releases of the quaternion package - -=============================================================================== -quaternion-2.0.0 Release Date: 2012-03-28 Release Manager: Lukas Reichlin -=============================================================================== - -** First official release. Its main features are: - -- Matrices and n-dimensional arrays of quaternions. - -- Overloaded operators due to the use of classes. - -- Operator semantics similar to Octave’s built-in complex numbers. - -- Vectorized code for crunching large quaternion arrays in a speedy manner. - - -===============================================================================
--- a/extra/quaternion_oo/devel/INFO Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,3 +0,0 @@ -With the current Makefile, the folder "devel" and its content -is ignored by "pkg install". The folder is intended for draft -code and other stuff which is not suitable for "normal" users. \ No newline at end of file
--- a/extra/quaternion_oo/devel/PROJECTS Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,54 +0,0 @@ -<html> -<pre> -Quaternion PROJECTS -*- text -*- -=================== - -grep FIXME and/or TODO for more information - - -------- -General: -------- - - * Add missing features to quaternion_oo such that it can replace quaternion-1.0.0. - - * Rename the existion main/quaternion package to extra/quaternion-legacy. - Rename extra/quaternion_oo to main/quaternion and release it as quaternion-2.0.0. - - * See if LaTEX code from Scottedward Hodel's quaternion.ps document is available. - Update it to use the commands from quaternion-2.0.0. - - * Secret Wish: Reimplement package completely in C++ similar to the sparsersb package ;-) - --------- -Features: --------- - - * Implement mpower. - - * Inverses of quaternion arrays. - - * Add functionality of qderiv and qtrans from quaternion-1.0.0. - - * Finish q2rot and rot2q. - ------- -Always: ------- - - * Squash bugs. - - * Write/improve documentation. If you implement a feature without documentation, - nobody besides you will ever use it! Don't waste your time :-) - - * Add description of each input and output argument to texinfo strings of - functions on the INDEX list. - - * Add tests. - - * Test the quaternion package on different platforms. - - * Compare results to those from other toolboxes like QTFM. - -</pre> -</html>
--- a/extra/quaternion_oo/devel/RELEASE_PACKAGE Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,46 +0,0 @@ -===================================================================================== -Prepare quaternion-2.x.y Package for Release -===================================================================================== -USAGE: * adapt all paths to your machine - * update version number in the commands below - * adapt version number and release date in DESCRIPTION - * update doc/NEWS - * adapt version number in quaternion.tex - * update doc/quaternion.pdf - * copy-paste entire block at once to the terminal - * follow instructions on <http://octave.sourceforge.net/developers.html> - -TODO: * create a nice shell script for this task -===================================================================================== - -cd -mkdir ~/octave/__TEMP__ -cd -svn export quaternion ~/octave/__TEMP__/quaternion -rm -R ~/octave/__TEMP__/quaternion/devel -cd ~/octave/__TEMP__ -grep -i version quaternion/DESCRIPTION -tar czf quaternion-2.0.0.tar.gz quaternion/ -md5 quaternion-2.0.0.tar.gz -md5 quaternion-2.0.0.tar.gz > md5_quaternion_pkg.txt -uuencode quaternion-2.0.0.tar.gz < quaternion-2.0.0.tar.gz > quaternion-2.0.0.tar.gz.uue -octave -q --eval \ -"pkg install quaternion-2.0.0.tar.gz" -octave -q --eval \ -"pkg load generate_html; generate_package_html ('quaternion', 'quaternion-html', 'octave-forge')" -tar czf quaternion-html.tar.gz quaternion-html -md5 quaternion-html.tar.gz -md5 quaternion-html.tar.gz > md5_quaternion_html.txt -uuencode quaternion-html.tar.gz < quaternion-html.tar.gz > quaternion-html.tar.gz.uue -cd - - -===================================================================================== -Aftermath -===================================================================================== - -rm -R ~/octave/__TEMP__ -rm -R ~/octave/quaternion-2.0.0 - - -=====================================================================================
--- a/extra/quaternion_oo/devel/RV9_Quaternions.txt Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,138 +0,0 @@ -%% Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch> -%% -%% This program is free software: you can redistribute it and/or modify -%% it under the terms of the GNU General Public License as published by -%% the Free Software Foundation, either version 3 of the License, or -%% any later version. -%% -%% This program is distributed in the hope that it will be useful, -%% but WITHOUT ANY WARRANTY; without even the implied warranty of -%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -%% GNU General Public License for more details. -%% -%% You should have received a copy of the GNU General Public License -%% along with this program. If not, see <http://www.gnu.org/licenses/>. - -=== Robotics Toolbox Port to Octave === -http://petercorke.com/Robotics_Toolbox.html -With the objective of porting the robotics toolbox version 9 to octave forge -we list the classes relate to quaternions. - -The idea is to see when this class has been fully ported, that is: - For a method x of the quaternion class, there is a method y in the - quaterions_oo package that - 1.Method y produces output isomorphic to output of x. - 2.Method y receives input isomorphic to input of method y. - - When the method y exist such that fullfils 1. and 2.; we say there is - an equivalent method in the packages quaternions_oo. - - If additonally the method y in the quaternions_oo package has the same name, - then we say that the method x exists in the package. - -The naming of the methods is not important, since the Robotics Toolbox for octave -will have a wrapper class quaternion. This class will emulate the API. - - -object.method(args) - -using the trick used here -[ http://octave.svn.sf.net/viewvc/octave/trunk/octave-forge/main/geometry/inst/io/%40svg/subsref.m?revision=8974&view=markup ] - -= Marking convention = -In the [] field of each method/operator/property add - - e - There is an isomorphic method (equivalent). - x - There is an isomorphic method with the same name (exist). - * - There is an exact equal method in the package (same input, output and name). - b+ - Benchmarked, slower than current method in quaternions_oo. - b- - Benchmarked, faster than current - - c - There is a method with the same name but not isomorphic (conflict). - -Example 1: -A method qc = qconj(q) exist in quaternions_oo that calculates the inverse of a quaternion. -Then we mark inv as follows - - [e] inv - - - Example 2: - A method [h a] = dosomething(q) from in quaternions_oo to calculate something. - The method [h] = somethingtodo(q) from Robotics toolbox to calculate the same. - - [e] somethingtodo - - Since the first argument is the same. - The same holds ff [a h] = dosomething(q). Since we need just to swap output arguemnts. - - - Example 3: - A method [h] = dosomething(q) from in quaternions_oo to calculate something. - The method [h a] = somethingtodo(q) from Robotics toolbox to calculate the same. - - [ ] somethingtodo - - Since we need to check how to calculate the output a. - - - Example 4: - A method [h] = dosomething(q) from in quaternions_oo to calculate something. - The method [h a] = somethingtodo(q) from Robotics toolbox to calculate the same. - And you benchmarked the methods givin a positive result for the quaternions_oo. - - [b+] somethingtodo - - The b flag indicates that there is a point of comparision but the methods may not be equivalent. - - - Example 4: - A method [h] = dosomething(q) from in quaternions_oo to calculate something. - The method [h] = dosomething(q) from Robotics toolbox to calculate the same. - And you benchmarked the methods givin a positive result for the robotics toolbox. - - [*b-] dosomething - - just concatenate flags. - -We hope not to run into the c tag. - -== Quaternion == -DONE Q = Quaternion() is the identitity quaternion 1<0,0,0> representing a null rotation. - -DONE Q = Quaternion(Q1) is a copy of the quaternion Q1 - -DONE Q = Quaternion([S V1 V2 V3]) is a quaternion formed by specifying directly its 4 elements - -DONE Q = Quaternion(S) is a quaternion formed from the scalar S and zero vector part: S<0,0,0> - -DONE Q = Quaternion(V) is a pure quaternion with the specified vector part: 0<V> - -DONE Q = Quaternion(TH, V) is a unit quaternion corresponding to rotation of TH about the vector V. - -DONE Q = Quaternion(R) is a unit quaternion corresponding to the orthonormal rotation matrix R. - -DONE Q = Quaternion(T) is a unit quaternion equivalent to the rotational - -= methods = -DONE [c] inv return inverse of quaterion -DONE [e] norm: Wraps abs from quaternions_oo -DONE [x] dot derivative of quaternion with angular velocity w -DONE [c] display -DONE [] q2tr -DONE [*] unit return unit quaternion - -[] plot same options as trplot() -[] interp interpolation (slerp) between q and q2, 0<=s<=1 -[] scale interpolation (slerp) between identity and q, 0<=s<=1 - -= Operators = -DONE [*] q+q2 return elementwise sum of quaternions -DONE [*] q-q2 return elementwise difference of quaternions -DONE [*] q*q2 return quaternion product -DONE [*] q/q2 return q*q2.inv - -[*] q*v rotate vector by quaternion, v is 3x1 -DONE [*] q^n return q to power n (real) - -= Properties (read only)= -DONE [] s real part -DONE [] v vector part -DONE [] R 3x3 rotation matrix -DONE [] T 4x4 homogeneous transform matrix
--- a/extra/quaternion_oo/devel/demoml.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,10 +0,0 @@ -q = rot2q ([0, 0, 1], pi/4) - -[vv, theta] = q2rot (q) - -x = quaternion (0, 1, 1, 0) % nicht normiert - % s x y z - -rx = q * x * conj (q) % q x q^-1 - -[vv, theta] = q2rot (rx)
--- a/extra/quaternion_oo/devel/generate_quaternion_pdf.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,12 +0,0 @@ -homedir = pwd (); -develdir = fileparts (which ("generate_quaternion_pdf")); -pdfdir = [develdir, "/pdfdoc"]; -cd (pdfdir); - -collect_texinfo_strings - -for i = 1:5 - system ("pdftex -interaction batchmode quaternion.tex"); -endfor - -cd (homedir);
--- a/extra/quaternion_oo/devel/makefile_quaternion.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -## ============================================================================== -## Developer Makefile for OCT-files -## ============================================================================== -## USAGE: * fetch quaternion_oo from Octave-Forge by svn -## * add quaternion_oo/inst, quaternion_oo/src and quaternion_oo/devel -## to your Octave path -## * run makefile_quaternion -## ============================================================================== - -homedir = pwd (); -develdir = fileparts (which ("makefile_quaternion")); -srcdir = [develdir, "/../src"]; -cd (srcdir); - -mkoctfile is_real_array.cc - -system ("rm *.o"); -cd (homedir); \ No newline at end of file
--- a/extra/quaternion_oo/devel/pdfdoc/collect_texinfo_strings.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,41 +0,0 @@ -% pack_name = "generate_html" -% pack_name = "control" -pack_name = "quaternion" - - -% Load Packages -pkg load "generate_html" -pkg ("load", pack_name); - -% Get list of functions -list = pkg ("describe", pack_name); - -%list - -% Open output file -fid = fopen ("functions.texi", "w"); - -for k = 1:numel (list {1}.provides) - - group = list {1}.provides{k}; - functions = group.functions; - - % fprintf (fid, '@section %s\n', group.category); - fprintf (fid, '@chapter %s\n', group.category); - - for k=1:numel(functions) - [TEXT, FORMAT] = get_help_text (functions(k)); - fun = functions{k}; - if (fun(1) == "@") - % fprintf (fid, '@subsection @%s\n', fun); - fprintf (fid, '@section @%s\n', fun); - else - % fprintf (fid, '@subsection %s\n', fun); - fprintf (fid, '@section %s\n', fun); - endif - fprintf (fid,TEXT); - end - -end - -fclose(fid);
--- a/extra/quaternion_oo/devel/pdfdoc/info_generate_manual.txt Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,13 +0,0 @@ -* Check that "pkg list" lists the packages generate_html and quaternion. -* Run collect_texinfo_strings within Octave. This script collects the Texinfo strings from all - functions listed in the package's INDEX file and writes them to the file functions.texi. - Don't edit the file functions.texi since your changes will be lost by the next run. -* Adapt version number in quaternion.tex -* Run quaternion.tex - - -pdftex quaternion.tex -q - -Alternatively: -Run generate_quaternion_pdf
--- a/extra/quaternion_oo/devel/pdfdoc/quaternion.tex Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,71 +0,0 @@ -\input texinfo @c -*-texinfo-*- -@c %**start of header -@setfilename quaternion.info -@settitle Octave Quaternion Package -@afourpaper -@set VERSION 2.0.0 -@finalout -@c @afourwide -@c %**end of header - -@c %*** Start of TITLEPAGE -@titlepage -@title quaternion @value{VERSION} -@subtitle Quaternion Package for GNU Octave -@author Lukas F. Reichlin -@author Juan Pablo Carbajal -@page -@vskip 0pt plus 1filll -Copyright @copyright{} 2010-2012, Lukas F. Reichlin @email{lukas.reichlin@@gmail.com} - -This manual is generated automatically from the texinfo help strings -of the package's functions. - -Permission is granted to make and distribute verbatim copies of -this manual provided the copyright notice and this permission notice -are preserved on all copies. - -Permission is granted to copy and distribute modified versions of this -manual under the conditions for verbatim copying, provided that the entire -resulting derived work is distributed under the terms of a permission -notice identical to this one. - -Permission is granted to copy and distribute translations of this manual -into another language, under the same conditions as for modified versions. -@page -@chapheading Preface -The @acronym{GNU} Octave quaternion package from version 2 onwards -was developed by Lukas F. Reichlin with important contributions by -Juan Pablo Carbajal. This new package is intended as a replacement -for quaternion-1.0.0 by A. Scottedward Hodel. It is loosely based -on ideas from the Quaternion Toolbox for Matlab by Steve Sangwine -and Nicolas Le Bihan with a special focus on code simplicity and -vectorization. Its main features are: -@itemize -@item Matrices and n-dimensional arrays of quaternions. -@item Overloaded operators due to the use of classes introduced with Octave 3.2. -@item Operator semantics similar to Octave's built-in complex numbers. -@item Fully vectorized code for crunching large quaternion arrays in a speedy manner. -@end itemize - - -@sp 5 -@subheading Using the help function -Some functions of the quaternion package are listed with a leading @code{@@quaternion/}. -This is only needed to view the help text of the function, e.g. @w{@code{help norm}} -shows the built-in function while @w{@code{help @@quaternion/norm}} shows the overloaded -function for quaternions. Note that there are quaternion functions -like @code{unit} that have no built-in equivalent. - -When just using the function, the leading @code{@@quaternion/} must @strong{not} be typed. -Octave selects the right function automatically. So one can type @w{@code{norm (q)}} -and @w{@code{norm (matrix)}} regardless of the class of the argument. -@end titlepage -@c %*** End of TITLEPAGE - -@contents -@c @chapter Function Reference -@include functions.texi - -@end -@bye
--- a/extra/quaternion_oo/devel/q0.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,9 +0,0 @@ -function q = q0 - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (1, 0, 0, 0); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/devel/q1.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,9 +0,0 @@ -function q = q1 - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (0, 1, 0, 0); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/devel/q2.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,9 +0,0 @@ -function q = q2 - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (0, 0, 1, 0); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/devel/q3.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,9 +0,0 @@ -function q = q3 - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (0, 0, 0, 1); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/devel/q4.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,9 +0,0 @@ -function q = q4 - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (1, 0, 0, 0); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/devel/q_2x2.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,10 +0,0 @@ -w = [2, 6; 10, 14]; - -x = [3, 7; 11, 15]; - -y = [4, 8; 12, 16]; - -z = [5, 9; 13, 17]; - -q = quaternion (w, x, y, z) -
--- a/extra/quaternion_oo/devel/q_2x3.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,10 +0,0 @@ -w = [2, 6, 10; 14, 18, 22]; - -x = [3, 7, 11; 15, 19, 23]; - -y = [4, 8, 12; 16, 20, 24]; - -z = [5, 9, 13; 17, 21, 25]; - -q = quaternion (w, x, y, z) -
--- a/extra/quaternion_oo/devel/qbug.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,3 +0,0 @@ -q = quaternion (2, 3, 4, 5) - -diag ([q, q, q]) \ No newline at end of file
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vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 0.00 deg) Cshow -2737 4900 M -(reference coordinates) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3631 2625 M --894 0 V -3631 2625 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -2252 2272 L -2737 2625 Pls -2252 2272 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M --177 970 V -2737 2625 Crs -2560 3595 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3631 2625 M --894 0 V -3631 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -2252 2272 L -2737 2625 Star -2252 2272 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M --177 970 V -2737 2625 Box -2560 3595 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --177 970 V --89 0 V -1.000 UL -LT3 -3323 1302 M --1789 0 V -1181 3242 L -970 706 V -1789 0 V -4293 2008 L -3323 1302 L -970 706 V --1788 0 V -2151 3948 L -2505 2008 L -1534 1302 L -1.000 UL -LT4 -3940 3948 M -2969 3242 L --1788 0 V -1788 0 V -3323 1302 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict 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a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 -b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p -Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(10)50 2045 -y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 -@rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 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-/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 10.00 deg) Cshow -2737 4900 M -(yaw=10.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3346 2535 M --609 90 V -3346 2535 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -749 508 V -2737 2625 Pls -3486 3133 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -83 9 V -8 11 V -5 9 V -0 8 V --4 7 V --8 5 V --11 2 V --15 1 V --17 -2 V --19 -4 V --21 -6 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly -410 @urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 15.00 deg) Cshow -2737 4900 M -(yaw=15.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3279 2491 M --542 134 V -3279 2491 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -800 499 V -2737 2625 Pls -3537 3124 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -87 14 V -7 10 V -2 9 V --1 7 V --6 6 V --9 4 V --13 2 V --16 -1 V --18 -3 V --20 -5 V --20 -6 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 20.00 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3207 2448 M --470 177 V -3207 2448 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -90 18 V -5 10 V -1 8 V --3 7 V --7 5 V --11 3 V --14 1 V --17 -2 V --19 -3 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial eop -11 10 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 -b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p -Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(11)50 2045 -y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 -@rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 20.00 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3207 2448 M --470 177 V -3207 2448 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -90 18 V -5 10 V -1 8 V --3 7 V --7 5 V --11 3 V --14 1 V --17 -2 V --19 -3 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 20.61 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch= 5.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3173 2527 M --436 98 V -3173 2527 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -405 -906 V -2737 2625 Crs -3142 1719 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --375 886 V -90 18 V -5 10 V -1 9 V --3 7 V --7 5 V --11 3 V --15 1 V --17 -1 V --18 -4 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly -410 @urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 22.34 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch=10.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3136 2606 M --399 19 V -3136 2606 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -441 -911 V -2737 2625 Crs -3178 1714 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --384 878 V -89 18 V -6 11 V -0 9 V --3 7 V --7 5 V --11 3 V --15 1 V --16 -1 V --19 -4 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 24.95 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch=15.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3096 2686 M --359 -61 V -3096 2686 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -474 -909 V -2737 2625 Crs -3211 1716 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --394 870 V -90 18 V -5 11 V -1 9 V --4 8 V --7 5 V --11 3 V --14 1 V --17 -1 V --19 -4 V --20 -6 V --19 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial eop -12 11 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 -b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p -Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(12)50 2045 -y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 -@rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 28.21 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch=20.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3054 2765 M -2737 2625 L -3054 2765 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -504 -901 V -2737 2625 Crs -3241 1724 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --403 861 V -89 19 V -5 11 V -1 10 V --3 7 V --7 6 V --11 3 V --15 1 V --16 -1 V --19 -4 V --20 -6 V --19 -9 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 28.71 deg) Cshow -2737 4900 M -(yaw=20.00, pitch=20.00, roll=10.00 \(deg\)) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3622 3070 M -2737 2625 L -3622 3070 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -236 176 V -2737 2625 Pls -2973 2801 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -476 -915 V -2737 2625 Crs -3213 1710 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3631 2625 M --894 0 V -3631 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -485 353 V -2737 2625 Star -3222 2978 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -177 -970 V -2737 2625 Box -2914 1655 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --140 990 V -100 8 V -2 6 V --2 5 V --7 4 V --11 3 V --14 2 V --18 1 V --19 0 V --21 -2 V --22 -3 V --21 -4 V -1.000 UL -LT3 -3323 1302 M --1789 0 V -1181 3242 L -970 706 V -1789 0 V -4293 2008 L -3323 1302 L -970 706 V --1788 0 V -2151 3948 L -2505 2008 L -1534 1302 L -1.000 UL -LT4 -3940 3948 M -2969 3242 L --1788 0 V -1788 0 V -3323 1302 L -stroke -grestore -end -showpage - @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly -410 @urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 30.19 deg) Cshow -2737 4900 M -(yaw=20.00, pitch=20.00, roll=15.00 \(deg\)) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3622 3070 M -2737 2625 L -3622 3070 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -277 95 V -2737 2625 Pls -3014 2720 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -454 -927 V -2737 2625 Crs -3191 1698 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3631 2625 M --894 0 V -3631 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -485 353 V -2737 2625 Star -3222 2978 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M 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M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 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bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 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bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 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y(6)1011 4168 y(6)1011 -4221 y(4)1125 3996 y Fq(_)-42 b Fo(q)1149 4011 y Fh(b)p -Fk(1)1125 4109 y Fq(_)g Fo(q)1149 4124 y Fh(b)p Fk(2)1125 -4222 y Fq(_)g Fo(q)1149 4237 y Fh(b)p Fk(3)1125 4335 -y Fq(_)g Fo(q)1149 4350 y Fh(b)p Fk(4)1260 3922 y Fi(3)1260 -4068 y(7)1260 4118 y(7)1260 4168 y(7)1260 4221 y(5)1340 -4166 y Fq(=)1446 4104 y Fo(!)p 1446 4145 V 1453 4228 -a Fq(2)1531 3922 y Fi(2)1531 4068 y(6)1531 4118 y(6)1531 -4168 y(6)1531 4221 y(4)1688 3996 y Fq(0)180 b Fo(!)1970 -4010 y Fk(3)2127 3996 y Fl(\000)p Fo(!)2255 4010 y Fk(2)2377 -3996 y Fo(!)2434 4010 y Fk(1)1628 4109 y Fl(\000)p Fo(!)1756 -4123 y Fk(3)1938 4109 y Fq(0)g Fo(!)2220 4123 y Fk(1)2377 -4109 y Fo(!)2434 4123 y Fk(2)1663 4222 y Fo(!)1720 4236 -y Fk(2)1878 4222 y Fl(\000)p Fo(!)2006 4236 y Fk(1)2188 -4222 y Fq(0)144 b Fo(!)2434 4236 y Fk(3)1628 4335 y Fl(\000)p -Fo(!)1756 4349 y Fk(1)1878 4335 y Fl(\000)p Fo(!)2006 -4349 y Fk(2)2127 4335 y Fl(\000)p Fo(!)2255 4349 y Fk(3)2402 -4335 y Fq(0)2515 3922 y Fi(3)2515 4068 y(7)2515 4118 -y(7)2515 4168 y(7)2515 4221 y(5)2585 3922 y(2)2585 4068 -y(6)2585 4118 y(6)2585 4168 y(6)2585 4221 y(4)2682 3996 -y Fo(q)2723 4011 y Fh(b)p Fk(1)2682 4109 y Fo(q)2723 -4124 y Fh(b)p Fk(2)2682 4222 y Fo(q)2723 4237 y Fh(b)p -Fk(3)2682 4335 y Fo(q)2723 4350 y Fh(b)p Fk(4)2834 3922 -y Fi(3)2834 4068 y(7)2834 4118 y(7)2834 4168 y(7)2834 -4221 y(5)0 4522 y Fq(Notice)31 b(that)g(the)g(4)21 b -Fl(\002)e Fq(4)31 b(matrix)f(is)f(sk)m(ew)i(symmetric)f(\(hence)h(its)e -(matrix)h(exp)s(onen)m(tial)f(is)h(orthogonal\).)0 4806 -y Fp(References)0 5009 y Fq([Mul])127 b(Larry)30 b(Mullins.)37 -b(Course)30 b(4160:)43 b(Quaternions.)c(Course)30 b(notes.)0 -5192 y([R)-10 b(W91])47 b(M.)41 b(H.)g(Rheinfurth)d(and)h(H.)i(B.)g -(Wilson.)70 b(Metho)s(ds)40 b(of)h(applied)d(dynamics.)69 -b(T)-8 b(ec)m(hnical)40 b(Rep)s(ort)337 5305 y(NASA)30 -b(RP-1262,)j(NASA,)e(George)h(C.)e(Marshall)f(Space)h(Fligh)m(t)g(Cen)m -(ter,)h(1991.)p eop -14 13 bop 0 527 a Fp(Index)0 709 y Fq(conjugate)166 821 -y(quaternion,)30 b(3)0 1017 y(Euler)f(angles)166 1130 -y(quaternions,)g(6)0 1326 y(Octa)m(v)m(e)166 1439 y Fj(qinv)p -Fq(,)h(3)166 1552 y Fj(qmult)p Fq(,)f(3)166 1665 y Fj(qtrans)p -Fq(,)g(4)166 1778 y(qtransv,)h(8)166 1891 y(qtransvmat,)h(8)166 -2004 y Fj(quaternion)p Fq(,)d(2)0 2200 y(quaternions)166 -2313 y(as)j(co)s(ordinate)f(rotations,)h(3)166 2425 y(co)s(ordinate)f -(transformation,)g(4)166 2538 y(co)s(ordinate)g(transformation)g -(matrices,)h(6)166 2651 y(cross)g(pro)s(ducts,)e(2)166 -2764 y(de\014nition,)f(2)166 2877 y(deriv)-5 b(ativ)m(es,)30 -b(12)166 2990 y(Euler)f(angles,)h(6)166 3103 y(m)m(ultiplication,)e(2) -166 3216 y(unit)h(quaternions,)g(3)1905 5656 y(14)p eop -end -userdict /end-hook known{end-hook}if
--- a/extra/quaternion_oo/devel/quaternion_arrays.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,58 +0,0 @@ -i = ones (3, 3); - -w = 2*i; -x = 3*i; -y = 4*i; -z = 5*i; - -q = quaternion (w, x, y, z) - -q .* conj (q) - - -%{ - -octave:1> quaternion_matrices -q.w = - 2 2 2 - 2 2 2 - 2 2 2 - -q.x = - 3 3 3 - 3 3 3 - 3 3 3 - -q.y = - 4 4 4 - 4 4 4 - 4 4 4 - -q.z = - 5 5 5 - 5 5 5 - 5 5 5 - -ans.w = - 54 54 54 - 54 54 54 - 54 54 54 - -ans.x = - 0 0 0 - 0 0 0 - 0 0 0 - -ans.y = - 0 0 0 - 0 0 0 - 0 0 0 - -ans.z = - 0 0 0 - 0 0 0 - 0 0 0 - -octave:2> - -%} \ No newline at end of file
--- a/extra/quaternion_oo/inst/@quaternion/abs.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,38 +0,0 @@ -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{qabs} =} abs (@var{q}) -## Modulus of a quaternion. -## -## @example -## q = w + x*i + y*j + z*k -## abs (q) = sqrt (w.^2 + x.^2 + y.^2 + z.^2) -## @end example -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: August 2010 -## Version: 0.2 - -function b = abs (a) - - if (nargin != 1) - print_usage (); - endif - - b = sqrt (norm2 (a)); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/blkdiag.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,60 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{q} =} blkdiag (@var{q1}, @var{q2}, @dots{}) -## Block-diagonal concatenation of quaternions. -## @end deftypefn - - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: December 2011 -## Version: 0.1 - -function q = blkdiag (varargin) - - tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! - - w = blkdiag (tmp.w); - x = blkdiag (tmp.x); - y = blkdiag (tmp.y); - z = blkdiag (tmp.z); - - q = quaternion (w, x, y, z); - -endfunction - - -%!shared C, D -%! Aw = [2, 6; 10, 14]; -%! Ax = [3, 7; 11, 15]; -%! Ay = [4, 8; 12, 16]; -%! Az = [5, 9; 13, 17]; -%! A = quaternion (Aw, Ax, Ay, Az); -%! -%! Bw = [2, 6, 10; 14, 18, 22]; -%! Bx = [3, 7, 11; 15, 19, 23]; -%! By = [4, 8, 12; 16, 20, 24]; -%! Bz = [5, 9, 13; 17, 21, 25]; -%! B = quaternion (Bw, Bx, By, Bz); -%! -%! C = blkdiag (A, B); -%! -%! Dw = blkdiag (Aw, Bw); -%! Dx = blkdiag (Ax, Bx); -%! Dy = blkdiag (Ay, By); -%! Dz = blkdiag (Az, Bz); -%! D = quaternion (Dw, Dx, Dy, Dz); -%!assert (C == D);
--- a/extra/quaternion_oo/inst/@quaternion/cat.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,36 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{q} =} cat (@var{dim}, @var{q1}, @var{q2}, @dots{}) -## Concatenation of quaternions along dimension @var{dim}. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function q = cat (dim, varargin) - - tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! - - w = cat (dim, tmp.w); - x = cat (dim, tmp.x); - y = cat (dim, tmp.y); - z = cat (dim, tmp.z); - - q = quaternion (w, x, y, z); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/columns.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,34 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{nc} =} columns (@var{q}) -## Return number of columns @var{nc} of quaternion array @var{q}. -## @end deftypefn - - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function c = columns (a) - - if (nargin != 1) - print_usage (); - endif - - c = columns (a.w); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/conj.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,40 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{q} =} conj (@var{q}) -## Return conjugate of a quaternion. -## -## @example -## q = w + x*i + y*j + z*k -## conj (q) = w - x*i - y*j - z*k -## @end example -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = conj (a) - - if (nargin != 1) - print_usage (); - endif - - a.x = -a.x; - a.y = -a.y; - a.z = -a.z; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/ctranspose.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,31 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Conjugate transpose of a quaternion. Used by Octave for "q'". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = ctranspose (a) - - if (nargin != 1) - print_usage (); - endif - - a = conj (transpose (a)); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/diag.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,53 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{q} =} diag (@var{v}) -## @deftypefnx {Function File} {@var{q} =} diag (@var{v}, @var{k}) -## Return a diagonal quaternion matrix with quaternion vector V on diagonal K. -## The second argument is optional. If it is positive, -## the vector is placed on the K-th super-diagonal. -## If it is negative, it is placed on the -K-th sub-diagonal. -## The default value of K is 0, and the vector is placed -## on the main diagonal. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = diag (a, b = 0) - - if (nargin == 0 || nargin > 2) - print_usage (); - endif - - a.w = diag (a.w, b); - a.x = diag (a.x, b); - a.y = diag (a.y, b); - a.z = diag (a.z, b); - -endfunction - - -%!shared R, S -%! Q = quaternion (2, 3, 4, 5); -%! R = diag ([Q, Q, Q]); -%! W = diag ([2, 2, 2]); -%! X = diag ([3, 3, 3]); -%! Y = diag ([4, 4, 4]); -%! Z = diag ([5, 5, 5]); -%! S = quaternion (W, X, Y, Z); -%!assert (R == S);
--- a/extra/quaternion_oo/inst/@quaternion/diff.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,64 +0,0 @@ -## Copyright (c) 1998, 2000, 2005, 2007 Auburn University. -## Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch> -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{qdot} =} diff (@var{q}, @var{omega}) -## Derivative of a quaternion. -## -## Let Q be a quaternion to transform a vector from a fixed frame to -## a rotating frame. If the rotating frame is rotating about the -## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative -## of Q is given by -## -## @example -## Q' = diff(Q, omega) -## @end example -## -## If the passive convention is used (rotate the frame, not the vector), -## then -## -## @example -## Q' = diff(Q,-omega) -## @end example -## @end deftypefn - -## Adapted from: qderiv by A. S. Hodel <a.s.hodel@eng.auburn.edu> - -function qd = diff (q, Omega) - - if (nargin != 2) - print_usage (); - endif - - if (! isa (q, "quaternion") || ! isscalar (q.w)) - error ("quaternion: first argument '%s' must be a scalar quaternion", inputname(1)); - endif - - Omega = vec (Omega); - - if (length (Omega) != 3) - error ("quaternion: second argument '%s' must be a length 3 vector", inputname(2)); - endif - - qd = 0.5 * quaternion (Omega(1), Omega(2), Omega(3)) * q; - -endfunction - -%!shared q -%! q = quaternion(3,1,0,0); - -%!assert(quaternion(0,0,0.5,1.5) == diff(q,[0 0 1])) -%!assert(quaternion(0,0,2,1) == diff(q,[0 1 1]))
--- a/extra/quaternion_oo/inst/@quaternion/display.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,63 +0,0 @@ -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Display routine for quaternions. Used by Octave internally. - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.2 - -function display (q) - - name = inputname(1); - s = size (q); - - if (length (s) == 2 && all (s == 1)) # scalar quaternion - w = num2str (q.w, 4); - x = __num2str__ (q.x); - y = __num2str__ (q.y); - z = __num2str__ (q.z); - disp ([name, " = ", w, x, "i" y, "j", z, "k"]); - disp (""); - else # non-scalar quaternion - disp ([name, ".w ="]); - disp (q.w); - disp (""); - disp ([name, ".x ="]); - disp (q.x); - disp (""); - disp ([name, ".y ="]); - disp (q.y); - disp (""); - disp ([name, ".z ="]); - disp (q.z); - disp (""); - endif - -endfunction - - -function str = __num2str__ (num) - - if (sign (num) == -1) - str = " - "; - else - str = " + "; - endif - - str = [str, num2str(abs (num), 4)]; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/eq.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,35 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Equal to operator for two quaternions. Used by Octave for "q1 == q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function flg = eq (a, b) - - if (! isa (a, "quaternion")) - a = quaternion (a); - endif - - if (! isa (b, "quaternion")) - b = quaternion (b); - endif - - flg = (a.w == b.w) && (a.x == b.x) && (a.y == b.y) && (a.z == a.z); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/exp.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,40 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{qexp} =} exp (@var{q}) -## Exponential of a quaternion. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function q = exp (q) - - if (nargin != 1) - print_usage (); - endif - - normv = normv (q); - exps = exp (q.w); - sinv = sin (normv); - - q.w = exps .* cos (normv); - q.x = exps .* (q.x ./ normv) .* sinv; - q.y = exps .* (q.y ./ normv) .* sinv; - q.z = exps .* (q.z ./ normv) .* sinv; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/horzcat.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,34 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Horizontal concatenation of quaternions. Used by Octave for "[q1, q2]". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = horzcat (varargin) - - tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! - - w = horzcat (tmp.w); - x = horzcat (tmp.x); - y = horzcat (tmp.y); - z = horzcat (tmp.z); - - q = quaternion (w, x, y, z); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/inv.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,42 +0,0 @@ -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{qinv} =} inv (@var{q}) -## Return inverse of a quaternion. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.2 - -function a = inv (a) - - if (nargin != 1) - print_usage (); - endif - - if (isscalar (a.w)) - norm2 = norm2 (a); - a.w = a.w / norm2; - a.x = -a.x / norm2; - a.y = -a.y / norm2; - a.z = -a.z / norm2; - else - ## TODO: quaternion arrays - error ("quaternion: inv: implemented for scalar quaternions only"); - endif - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/ispure.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,33 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{flg} =} ispure (@var{q}) -## Return 1 if scalar part of quaternion is zero, otherwise return 0 -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function flg = ispure (a) - - if (nargin != 1) - print_usage (); - endif - - flg = all ((abs (a.w) < eps)(:)); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/ldivide.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,27 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Element-wise left division for quaternions. Used by Octave for "q1 .\\ q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = ldivide (a, b) - - q = a.^-1 .* b; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/log.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,61 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{qlog} =} log (@var{q}) -## Logarithmus naturalis of a quaternion. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function q = log (q) - - if (nargin != 1) - print_usage (); - endif - - normq = abs (q); - normv = normv (q); - acossq = acos (q.w ./ normq); - - q.w = log (normq); - q.x = (q.x ./ normv) .* acossq; - q.y = (q.y ./ normv) .* acossq; - q.z = (q.z ./ normv) .* acossq; - - ## FIXME: q = quaternion (2, 3, 4, 5) - ## p = log (exp (q)) - ## p.v is wrong, probably somehow related to acos - ## NOTE: p = exp (log (q)) is calculated correctly - ## NOTE: qtfm 1.9 returns the same "wrong" result - -endfunction - - -%!shared A, B -%! Aw = [2, 6, 10; 14, 18, 22]; -%! Ax = [3, 7, 11; 15, 19, 23]; -%! Ay = [4, 8, 12; 16, 20, 24]; -%! Az = [5, 9, 13; 17, 21, 25]; -%! A = quaternion (Aw, Ax, Ay, Az); -%! -%! B = exp (log (A)); -%! -%!assert (A.w, B.w, 1e-4); -%!assert (A.x, B.x, 1e-4); -%!assert (A.y, B.y, 1e-4); -%!assert (A.z, B.z, 1e-4);
--- a/extra/quaternion_oo/inst/@quaternion/minus.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,38 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Subtraction of two quaternions. Used by Octave for "q1 - q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = minus (a, b) - - if (! isa (a, "quaternion")) - a = quaternion (a); - endif - - if (! isa (b, "quaternion")) - b = quaternion (b); - endif - - a.w = a.w - b.w; - a.x = a.x - b.x; - a.y = a.y - b.y; - a.z = a.z - b.z; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/mldivide.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,27 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Matrix left division for quaternions. Used by Octave for "q1 \\ q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = mldivide (a, b) - - q = inv (a) * b; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/mpower.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,56 +0,0 @@ -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Matrix power operator of quaternions. Used by Octave for "q^x". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.2 - -function q = mpower (a, b) - - [r, c] = size (a); - - if (r != c) - error ("quaternion: mpower: quaternion matrix must be square"); - endif - - if (r == 1 && c == 1) # a scalar, b? - q = a .^ b; # b could be a quaternion - elseif (is_real_array (b) && isscalar (b) && fix (b) == b) - e = fix (abs (b)); - switch (sign (b)) - case -1 # q^-e - a = inv (a); - q = a; - case 0 # q^0 - q = eye (r); # alternative: q = quaternion (eye (r)) - return; - case 1; # q^e - q = a; - endswitch - for k = 2 : e - q *= a; # improvement?: q^8 = ((q^2)^2)^2, q^9 = (((q^2)^2)^2)*q - endfor - else - error ("quaternion: mpower: case not implemented yet"); - q = expm (logm (a) * b); # don't know whether this formula is correct - endif - - ## TODO: - q1 ^ q2 - ## - arrays - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/mrdivide.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,27 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Matrix right division for quaternions. Used by Octave for "q1 / q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = mrdivide (a, b) - - q = a * inv (b); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/mtimes.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,43 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Matrix multiplication of two quaternions. Used by Octave for "q1 * q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = mtimes (a, b) - - if (! isa (a, "quaternion")) - a = quaternion (a); - endif - - if (! isa (b, "quaternion")) - b = quaternion (b); - endif - - w = a.w*b.w - a.x*b.x - a.y*b.y - a.z*b.z; - x = a.y*b.z - a.z*b.y + a.w*b.x + a.x*b.w; - y = a.z*b.x - a.x*b.z + a.w*b.y + a.y*b.w; - z = a.x*b.y - a.y*b.x + a.w*b.z + a.z*b.w; - - a.w = w; - a.x = x; - a.y = y; - a.z = z; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/norm.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,38 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{n} =} norm (@var{q}) -## Norm of a quaternion. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function n = norm (a) - - if (nargin != 1) - print_usage (); - endif - - if (! isscalar (a.w)) - warning ("norm: use 'abs' to calculate the lengths of quaternion arrays"); - error ("norm: only the 2-norm of scalar quaternions is implemented until now"); - endif - - n = abs (a); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/plus.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,38 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Addition of two quaternions. Used by Octave for "q1 + q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = plus (a, b) - - if (! isa (a, "quaternion")) - a = quaternion (a); - endif - - if (! isa (b, "quaternion")) - b = quaternion (b); - endif - - a.w = a.w + b.w; - a.x = a.x + b.x; - a.y = a.y + b.y; - a.z = a.z + b.z; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/power.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,49 +0,0 @@ -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch> -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Power operator of quaternions. Used by Octave for "q.^x". -## Exponent x can be scalar or of appropriate size. - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.3 - -function a = power (a, b) - - if (isa (b, "quaternion")) # exponent is a quaternion - a = exp (log (a) .* b); # a could be real, but log doesn't care - elseif (! isreal (b)) - error ("quaternion:invalidArgument", "quaternion: power: invalid exponent"); - elseif (b == -1) # special case for ldivide and rdivide - norm2 = norm2 (a); # a is quaternion because b is not, - a.w = a.w ./ norm2; # otherwise octave wouldn't call - a.x = -a.x ./ norm2; # quaternion's power operator. - a.y = -a.y ./ norm2; - a.z = -a.z ./ norm2; - else # exponent is real - na = abs (a); - nv = normv (a); - th = acos (a.w ./ na); - nab = na.^b; - snt = sin (b.*th); - a.w = nab .* cos (b.*th); - a.x = (a.x ./ nv) .* nab .* snt; - a.y = (a.y ./ nv) .* nab .* snt; - a.z = (a.z ./ nv) .* nab .* snt; - endif - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/private/norm2.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,29 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{norm2} =} norm2 (@var{q}) -## Return squared norm of a quaternion. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function ret = norm2 (a) - - ret = a.w.^2 + a.x.^2 + a.y.^2 + a.z.^2; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/private/normv.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,29 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{normv} =} normv (@var{q}) -## Return norm of the vector part. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function ret = normv (a) - - ret = sqrt (a.x.^2 + a.y.^2 + a.z.^2); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/quaternion.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,111 +0,0 @@ -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{q} =} quaternion (@var{w}) -## @deftypefnx {Function File} {@var{q} =} quaternion (@var{x}, @var{y}, @var{z}) -## @deftypefnx {Function File} {@var{q} =} quaternion (@var{w}, @var{x}, @var{y}, @var{z}) -## Constructor for quaternions - create or convert to quaternion. -## -## @example -## q = w + x*i + y*j + z*k -## @end example -## -## Arguments @var{w}, @var{x}, @var{y} and @var{z} can be scalars or -## matrices, but they must be real and of equal size. If scalar part -## @var{w} or components @var{x}, @var{y} and @var{z} of the vector -## part are not specified, zero matrices of appropriate size are -## assumed. -## -## @strong{Example} -## @example -## @group -## octave:1> q = quaternion (2) -## q = 2 + 0i + 0j + 0k -## -## octave:2> q = quaternion (3, 4, 5) -## q = 0 + 3i + 4j + 5k -## -## octave:3> q = quaternion (2, 3, 4, 5) -## q = 2 + 3i + 4j + 5k -## @end group -## @end example -## @example -## @group -## octave:4> w = [2, 6, 10; 14, 18, 22]; -## octave:5> x = [3, 7, 11; 15, 19, 23]; -## octave:6> y = [4, 8, 12; 16, 20, 24]; -## octave:7> z = [5, 9, 13; 17, 21, 25]; -## octave:8> q = quaternion (w, x, y, z) -## q.w = -## 2 6 10 -## 14 18 22 -## -## q.x = -## 3 7 11 -## 15 19 23 -## -## q.y = -## 4 8 12 -## 16 20 24 -## -## q.z = -## 5 9 13 -## 17 21 25 -## -## octave:9> -## @end group -## @end example -## -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.2 - -function q = quaternion (a, b, c, d) - - switch (nargin) - case 1 - if (isa (a, "quaternion")) # quaternion (q) - q = a; - return; - elseif (is_real_array (a)) # quaternion (w) - b = c = d = zeros (size (a)); - else - print_usage (); - endif - case 3 # quaternion (x, y, z) - d = c; - c = b; - b = a; - a = zeros (size (a)); - case 4 # quaternion (w, x, y, z) - ## nothing to do here, just prevent case "otherwise" - otherwise - print_usage (); - endswitch - - if (! is_real_array (a, b, c, d)) - error ("quaternion: arguments must be real matrices"); - endif - - if (! size_equal (a, b, c, d)); - error ("quaternion: arguments must have identical sizes"); - endif - - q = class (struct ("w", a, "x", b, "y", c, "z", d), "quaternion"); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/rdivide.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,27 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Element-wise right division for quaternions. Used by Octave for "q1 ./ q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = rdivide (a, b) - - q = a .* b.^-1; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/rows.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,33 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{nr} =} rows (@var{q}) -## Return number of rows @var{nr} of quaternion array @var{q}. -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function r = rows (a) - - if (nargin != 1) - print_usage (); - endif - - r = rows (a.w); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/size.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,74 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{nvec} =} size (@var{q}) -## @deftypefnx {Function File} {@var{n} =} size (@var{q}, @var{dim}) -## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @dots{}] =} size (@var{q}) -## Return size of quaternion arrays. -## -## @strong{Inputs} -## @table @var -## @item q -## Quaternion object. -## @item dim -## If given a second argument, @command{size} will return the size of the -## corresponding dimension. -## @end table -## -## @strong{Outputs} -## @table @var -## @item nvec -## Row vector. The first element is the number of rows and the second -## element the number of columns. If @var{q} is an n-dimensional array -## of quaternions, the n-th element of @var{nvec} corresponds to the -## size of the n-th dimension of @var{q}. -## @item n -## Scalar value. The size of the dimension @var{dim}. -## @item nx -## Number of rows. -## @item ny -## Number of columns. -## @item @dots{} -## Sizes of the 3rd to n-th dimensions. -## @end table -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.2 - -function varargout = size (a, b) - - switch (nargout) - case {0, 1} - switch (nargin) - case 1 # nvec = size (q) - varargout{1} = size (a.w); - case 2 # n = size (q, dim) - varargout{1} = size (a.w, b); - otherwise - print_usage (); - endswitch - - otherwise - if (nargin == 1) # [nx, ny, ...] = size (q) - varargout = num2cell (size (a.w)); - else - print_usage (); - endif - endswitch - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/subsasgn.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,64 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Subscripted assignment for quaternions. -## Used by Octave for "q.key = value". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.2 - -function q = subsasgn (q, idx, val) - - switch (idx(1).type) - case "()" # q(...) = val - if (length (idx(1).subs) == 1 && isa (val, "quaternion")) # required by horzcat, vertcat, cat, ... - q(idx(1).subs{:}) = val; # q = cellfun (@quaternion, varargin) - else # general case - val = quaternion (val); - w = subsasgn (q.w, idx, val.w); - x = subsasgn (q.x, idx, val.x); - y = subsasgn (q.y, idx, val.y); - z = subsasgn (q.z, idx, val.z); - q = quaternion (w, x, y, z); - endif - - case "." # q.w = val - if (! is_real_array (val)) - error ("quaternion: subsasgn: invalid argument type, require real array"); - endif - if (! size_equal (subsref (q.w, idx(2:end)), val)) - error ("quaternion: subsasgn: invalid argument size [%s], require dimensions [%s]", \ - num2str (size (val), "%d "), num2str (size (subsref (q.w, idx(2:end))), "%d ")); - endif - switch (tolower (idx(1).subs)) - case {"w", "s"} - q.w = subsasgn (q.w, idx(2:end), val); - case {"x", "i"} - q.x = subsasgn (q.x, idx(2:end), val); - case {"y", "j"} - q.y = subsasgn (q.y, idx(2:end), val); - case {"z", "k"} - q.z = subsasgn (q.z, idx(2:end), val); - otherwise - error ("quaternion: subsasgn: invalid subscript name '%s'", idx(1).subs); - endswitch - - otherwise - error ("quaternion: subsasgn: invalid subscript type '%s'", idx(1).type); - endswitch - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/subsref.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,60 +0,0 @@ -## Copyright (C) 2010, 2011, 2012 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Subscripted reference for quaternions. Used by Octave for "q.w". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.4 - -function ret = subsref (q, s) - - if (numel (s) == 0) - ret = q; - return; - endif - - switch (s(1).type) - case "." # q.w - switch (tolower (s(1).subs)) - case {"w", "s"} # scalar part - ret = subsref (q.w, s(2:end)); - case {"x", "i"} - ret = subsref (q.x, s(2:end)); - case {"y", "j"} - ret = subsref (q.y, s(2:end)); - case {"z", "k"} - ret = subsref (q.z, s(2:end)); - case "v" # vector part, scalar part set to zero - q.w = zeros (size (q.w)); - ret = subsref (q, s(2:end)); - otherwise - error ("quaternion: invalid subscript name '%s'", s(1).subs); - endswitch - - case "()" # q(...) - w = subsref (q.w, s(1)); - x = subsref (q.x, s(1)); - y = subsref (q.y, s(1)); - z = subsref (q.z, s(1)); - tmp = quaternion (w, x, y, z); - ret = subsref (tmp, s(2:end)); - - otherwise - error ("quaternion: invalid subscript type '%s'", s(1).type); - endswitch - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/times.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,43 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Element-wise multiplication of two quaternions. Used by Octave for "q1 .* q2". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = times (a, b) - - if (! isa (a, "quaternion")) - a = quaternion (a); - endif - - if (! isa (b, "quaternion")) - b = quaternion (b); - endif - - w = a.w .* b.w - a.x .* b.x - a.y .* b.y - a.z .* b.z; - x = a.y .* b.z - a.z .* b.y + a.w .* b.x + a.x .* b.w; - y = a.z .* b.x - a.x .* b.z + a.w .* b.y + a.y .* b.w; - z = a.x .* b.y - a.y .* b.x + a.w .* b.z + a.z .* b.w; - - a.w = w; - a.x = x; - a.y = y; - a.z = z; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/transpose.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,34 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Transpose of a quaternion. Used by Octave for "q.'". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = transpose (a) - - if (nargin != 1) - print_usage (); - endif - - a.w = transpose (a.w); - a.x = transpose (a.x); - a.y = transpose (a.y); - a.z = transpose (a.z); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/uminus.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,30 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Unary minus of a quaternion. Used by Octave for "-q". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function a = uminus (a) - - a.w = -a.w; - a.x = -a.x; - a.y = -a.y; - a.z = -a.z; - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/unit.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,38 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{qn} =} unit (@var{q}) -## Normalize quaternion to length 1 (unit quaternion). -## -## @example -## q = w + x*i + y*j + z*k -## unit (q) = q ./ sqrt (w.^2 + x.^2 + y.^2 + z.^2) -## @end example -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function q = unit (a) - - if (nargin != 1) - print_usage (); - endif - - q = a ./ abs (a); - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/uplus.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,27 +0,0 @@ -## Copyright (C) 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Unary plus of a quaternion. Used by Octave for "+q". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: November 2011 -## Version: 0.1 - -function a = uplus (a) - - ## nothing to do here - -endfunction
--- a/extra/quaternion_oo/inst/@quaternion/vertcat.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,34 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## Vertical concatenation of quaternions. Used by Octave for "[q1; q2]". - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = vertcat (varargin) - - tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! - - w = vertcat (tmp.w); - x = vertcat (tmp.x); - y = vertcat (tmp.y); - z = vertcat (tmp.z); - - q = quaternion (w, x, y, z); - -endfunction
--- a/extra/quaternion_oo/inst/q2rot.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,93 +0,0 @@ -## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 Auburn University -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {[@var{axis}, @var{angle}] =} q2rot (@var{q}) -## Extract vector/angle form of a unit quaternion @var{q}. -## -## @strong{Inputs} -## @table @var -## @item q -## Unit quaternion describing the rotation. -## @end table -## -## @strong{Outputs} -## @table @var -## @item axis -## Eigenaxis as a 3-d unit vector @code{[x, y, z]}. -## @item angle -## Rotation angle in radians. The positive direction is -## determined by the right-hand rule applied to @var{axis}. -## @end table -## -## @strong{Example} -## @example -## @group -## octave:1> axis = [0, 0, 1] -## axis = -## 0 0 1 -## octave:2> angle = pi/4 -## angle = 0.78540 -## octave:3> q = rot2q (axis, angle) -## q = 0.9239 + 0i + 0j + 0.3827k -## octave:4> [vv, th] = q2rot (q) -## vv = -## 0 0 1 -## th = 0.78540 -## octave:5> theta = th*180/pi -## theta = 45.000 -## octave:6> -## @end group -## @end example -## -## @end deftypefn - -## Adapted from: quaternion by A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function [vv, theta] = q2rot (q) - - if (nargin != 1 || nargout != 2) - print_usage (); - endif - - if (! isa (q, "quaternion") || ! isscalar (q.w)) - error ("q2rot: require scalar quaternion as input"); - endif - - if (abs (norm (q) - 1) > 1e-12) - warning ("q2rot: ||q||=%e, setting=1 for vv, theta", norm (q)); - q = unit (q); - endif - - s = q.s; - vv = [q.x, q.y, q.z]; - - theta = acos (s) * 2; - - if (abs (theta) > pi) - theta = theta - sign (theta) * pi; - endif - - sin_th_2 = norm (vv); - - if (sin_th_2 != 0) - vv ./= sin_th_2; - endif - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/inst/qi.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,48 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## @deftypefn {Function File} {} qi -## Create x-component of a quaternion's vector part. -## -## @example -## q = w + x*qi + y*qj + z*qk -## @end example -## -## @strong{Example} -## @example -## @group -## octave:1> q1 = quaternion (1, 2, 3, 4) -## q1 = 1 + 2i + 3j + 4k -## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk -## q2 = 1 + 2i + 3j + 4k -## octave:3> -## @end group -## @end example -## -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = qi - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (0, 1, 0, 0); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/inst/qj.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,48 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## @deftypefn {Function File} {} qj -## Create y-component of a quaternion's vector part. -## -## @example -## q = w + x*qi + y*qj + z*qk -## @end example -## -## @strong{Example} -## @example -## @group -## octave:1> q1 = quaternion (1, 2, 3, 4) -## q1 = 1 + 2i + 3j + 4k -## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk -## q2 = 1 + 2i + 3j + 4k -## octave:3> -## @end group -## @end example -## -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = qj - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (0, 0, 1, 0); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/inst/qk.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,48 +0,0 @@ -## Copyright (C) 2010 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## @deftypefn {Function File} {} qk -## Create z-component of a quaternion's vector part. -## -## @example -## q = w + x*qi + y*qj + z*qk -## @end example -## -## @strong{Example} -## @example -## @group -## octave:1> q1 = quaternion (1, 2, 3, 4) -## q1 = 1 + 2i + 3j + 4k -## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk -## q2 = 1 + 2i + 3j + 4k -## octave:3> -## @end group -## @end example -## -## @end deftypefn - -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = qk - - if (nargin != 0) - print_usage (); - endif - - q = quaternion (0, 0, 0, 1); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/inst/rot2q.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,95 +0,0 @@ -## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 Auburn University -## Copyright (C) 2010, 2011 Lukas F. Reichlin -## -## This program is free software: you can redistribute it and/or modify -## it under the terms of the GNU General Public License as published by -## the Free Software Foundation, either version 3 of the License, or -## (at your option) any later version. -## -## This program is distributed in the hope that it will be useful, -## but WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -## GNU General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program. If not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{q} =} rot2q (@var{axis}, @var{angle}) -## Create unit quaternion @var{q} which describes a rotation of -## @var{angle} radians about the vector @var{axis}. This function uses -## the active convention where the vector @var{axis} is rotated by @var{angle} -## radians. If the coordinate frame should be rotated by @var{angle} -## radians, also called the passive convention, this is equivalent -## to rotating the @var{axis} by @var{-angle} radians. -## -## @strong{Inputs} -## @table @var -## @item axis -## Vector @code{[x, y, z]} describing the axis of rotation. -## @item angle -## Rotation angle in radians. The positive direction is -## determined by the right-hand rule applied to @var{axis}. -## @end table -## -## @strong{Outputs} -## @table @var -## @item q -## Unit quaternion describing the rotation. -## @end table -## -## @strong{Example} -## @example -## @group -## octave:1> axis = [0, 0, 1]; -## octave:2> angle = pi/4; -## octave:3> q = rot2q (axis, angle) -## q = 0.9239 + 0i + 0j + 0.3827k -## octave:4> v = quaternion (1, 1, 0) -## v = 0 + 1i + 1j + 0k -## octave:5> vr = q * v * conj (q) -## vr = 0 + 0i + 1.414j + 0k -## octave:6> -## @end group -## @end example -## -## @end deftypefn - -## Adapted from: quaternion by A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Author: Lukas Reichlin <lukas.reichlin@gmail.com> -## Created: May 2010 -## Version: 0.1 - -function q = rot2q (vv, theta) - - if (nargin != 2 || nargout != 1) - print_usage (); - endif - - if (! isvector (vv) || length (vv) != 3) - error ("vv must be a length three vector"); - endif - - if (! isscalar (theta)) - error ("theta must be a scalar"); - endif - - if (norm (vv) == 0) - error ("quaternion: vv is zero"); - endif - - if (abs (norm (vv) - 1) > 1e-12) - warning ("quaternion: ||vv|| != 1, normalizing") - vv = vv / norm (vv); - endif - - if (abs (theta) > 2*pi) - warning ("quaternion: |theta| > 2 pi, normalizing") - theta = rem (theta, 2*pi); - endif - - vv = vv * sin (theta / 2); - d = cos (theta / 2); - q = quaternion (d, vv(1), vv(2), vv(3)); - -endfunction \ No newline at end of file
--- a/extra/quaternion_oo/inst/test_quaternion.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,4 +0,0 @@ -test @quaternion/blkdiag -test @quaternion/diag -test @quaternion/diff -test @quaternion/log \ No newline at end of file
--- a/extra/quaternion_oo/src/Makefile Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,8 +0,0 @@ -all: is_real_array.oct - -# helper -is_real_array.oct: is_real_array.cc - mkoctfile is_real_array.cc - -clean: - rm *.o core octave-core *.oct *~
--- a/extra/quaternion_oo/src/is_real_array.cc Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,60 +0,0 @@ -/* - -Copyright (C) 2011 Lukas F. Reichlin - -This file is part of LTI Syncope. - -LTI Syncope is free software: you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation, either version 3 of the License, or -(at your option) any later version. - -LTI Syncope is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -You should have received a copy of the GNU General Public License -along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. - -Return true if argument is a real array. - -Author: Lukas Reichlin <lukas.reichlin@gmail.com> -Created: November 2011 -Version: 0.2 - -*/ - -#include <octave/oct.h> - -DEFUN_DLD (is_real_array, args, nargout, - "-*- texinfo -*-\n\ -@deftypefn {Loadable Function} {} is_real_array (@var{a}, @dots{})\n\ -Return true if argument is a real array.\n\ -@var{[]} is a valid array.\n\ -Avoid nasty stuff like @code{true = isreal (\"a\")}.\n\ -@end deftypefn") -{ - octave_value retval = true; - int nargin = args.length (); - - if (nargin == 0) - { - print_usage (); - } - else - { - for (int i = 0; i < nargin; i++) - { - // args(i).ndims () should be always >= 2 - if (args(i).ndims () < 2 || ! args(i).is_numeric_type () - || ! args(i).is_real_type ()) - { - retval = false; - break; - } - } - } - - return retval; -}
--- a/main/quaternion/DESCRIPTION Wed Mar 28 02:57:39 2012 +0000 +++ b/main/quaternion/DESCRIPTION Wed Mar 28 03:16:58 2012 +0000 @@ -1,13 +1,11 @@ Name: quaternion -Version: 1.0.0 -Date: 2008-07-17 -Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -Maintainer: The Octave-Forge Community -Title: Quaternion Package -Description: Package for the manipulation of Quaternion's used for - frame transformation -Categories: Mathematics -Depends: octave (>= 3.1.0) +Version: 2.0.0 +Date: 2012-03-28 +Author: Lukas Reichlin <lukas.reichlin@gmail.com> +Maintainer: Lukas Reichlin <lukas.reichlin@gmail.com> +Title: Quaternion +Description: Overloaded operators for quaternions +Depends: octave (>= 3.6.0) Autoload: yes License: GPL version 3 or later Url: http://octave.sf.net
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/INDEX Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,44 @@ +quaternion >> Quaternion +Quaternions + quaternion + qi + qj + qk + q2rot + rot2q +Methods + @quaternion/abs + @quaternion/blkdiag + @quaternion/cat + @quaternion/columns + @quaternion/conj + @quaternion/diag + @quaternion/diff + @quaternion/exp + @quaternion/inv + @quaternion/ispure + @quaternion/log + @quaternion/norm + @quaternion/rows + @quaternion/size + @quaternion/unit +Overloaded Operators + @quaternion/ctranspose + @quaternion/eq + @quaternion/horzcat + @quaternion/ldivide + @quaternion/minus + @quaternion/mldivide + @quaternion/mpower + @quaternion/mrdivide + @quaternion/mtimes + @quaternion/plus + @quaternion/power + @quaternion/rdivide + @quaternion/subsasgn + @quaternion/subsref + @quaternion/times + @quaternion/transpose + @quaternion/uminus + @quaternion/uplus + @quaternion/vertcat
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/Makefile Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,16 @@ +sinclude ../../Makeconf + +PKG_FILES = COPYING DESCRIPTION INDEX NEWS $(wildcard inst/*) +SUBDIRS = doc/ + +.PHONY: $(SUBDIRS) + +pre-pkg:: + @for _dir in $(SUBDIRS); do \ + $(MAKE) -C $$_dir all; \ + done + +clean: + @for _dir in $(SUBDIRS); do \ + $(MAKE) -C $$_dir $(MAKECMDGOALS); \ + done
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/NEWS Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,14 @@ +Summary of important user-visible changes for releases of the quaternion package + +=============================================================================== +quaternion-2.0.0 Release Date: 2012-03-28 Release Manager: Lukas Reichlin +=============================================================================== + +** First official release. Its main features are: + -- Matrices and n-dimensional arrays of quaternions. + -- Overloaded operators due to the use of classes. + -- Operator semantics similar to Octave’s built-in complex numbers. + -- Vectorized code for crunching large quaternion arrays in a speedy manner. + + +===============================================================================
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/INFO Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,3 @@ +With the current Makefile, the folder "devel" and its content +is ignored by "pkg install". The folder is intended for draft +code and other stuff which is not suitable for "normal" users. \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/PROJECTS Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,54 @@ +<html> +<pre> +Quaternion PROJECTS -*- text -*- +=================== + +grep FIXME and/or TODO for more information + + +------- +General: +------- + + * Add missing features to quaternion_oo such that it can replace quaternion-1.0.0. + + * Rename the existion main/quaternion package to extra/quaternion-legacy. + Rename extra/quaternion_oo to main/quaternion and release it as quaternion-2.0.0. + + * See if LaTEX code from Scottedward Hodel's quaternion.ps document is available. + Update it to use the commands from quaternion-2.0.0. + + * Secret Wish: Reimplement package completely in C++ similar to the sparsersb package ;-) + +-------- +Features: +-------- + + * Implement mpower. + + * Inverses of quaternion arrays. + + * Add functionality of qderiv and qtrans from quaternion-1.0.0. + + * Finish q2rot and rot2q. + +------ +Always: +------ + + * Squash bugs. + + * Write/improve documentation. If you implement a feature without documentation, + nobody besides you will ever use it! Don't waste your time :-) + + * Add description of each input and output argument to texinfo strings of + functions on the INDEX list. + + * Add tests. + + * Test the quaternion package on different platforms. + + * Compare results to those from other toolboxes like QTFM. + +</pre> +</html>
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/RELEASE_PACKAGE Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,46 @@ +===================================================================================== +Prepare quaternion-2.x.y Package for Release +===================================================================================== +USAGE: * adapt all paths to your machine + * update version number in the commands below + * adapt version number and release date in DESCRIPTION + * update doc/NEWS + * adapt version number in quaternion.tex + * update doc/quaternion.pdf + * copy-paste entire block at once to the terminal + * follow instructions on <http://octave.sourceforge.net/developers.html> + +TODO: * create a nice shell script for this task +===================================================================================== + +cd +mkdir ~/octave/__TEMP__ +cd +svn export quaternion ~/octave/__TEMP__/quaternion +rm -R ~/octave/__TEMP__/quaternion/devel +cd ~/octave/__TEMP__ +grep -i version quaternion/DESCRIPTION +tar czf quaternion-2.0.0.tar.gz quaternion/ +md5 quaternion-2.0.0.tar.gz +md5 quaternion-2.0.0.tar.gz > md5_quaternion_pkg.txt +uuencode quaternion-2.0.0.tar.gz < quaternion-2.0.0.tar.gz > quaternion-2.0.0.tar.gz.uue +octave -q --eval \ +"pkg install quaternion-2.0.0.tar.gz" +octave -q --eval \ +"pkg load generate_html; generate_package_html ('quaternion', 'quaternion-html', 'octave-forge')" +tar czf quaternion-html.tar.gz quaternion-html +md5 quaternion-html.tar.gz +md5 quaternion-html.tar.gz > md5_quaternion_html.txt +uuencode quaternion-html.tar.gz < quaternion-html.tar.gz > quaternion-html.tar.gz.uue +cd + + +===================================================================================== +Aftermath +===================================================================================== + +rm -R ~/octave/__TEMP__ +rm -R ~/octave/quaternion-2.0.0 + + +=====================================================================================
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/RV9_Quaternions.txt Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,138 @@ +%% Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch> +%% +%% This program is free software: you can redistribute it and/or modify +%% it under the terms of the GNU General Public License as published by +%% the Free Software Foundation, either version 3 of the License, or +%% any later version. +%% +%% This program is distributed in the hope that it will be useful, +%% but WITHOUT ANY WARRANTY; without even the implied warranty of +%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +%% GNU General Public License for more details. +%% +%% You should have received a copy of the GNU General Public License +%% along with this program. If not, see <http://www.gnu.org/licenses/>. + +=== Robotics Toolbox Port to Octave === +http://petercorke.com/Robotics_Toolbox.html +With the objective of porting the robotics toolbox version 9 to octave forge +we list the classes relate to quaternions. + +The idea is to see when this class has been fully ported, that is: + For a method x of the quaternion class, there is a method y in the + quaterions_oo package that + 1.Method y produces output isomorphic to output of x. + 2.Method y receives input isomorphic to input of method y. + + When the method y exist such that fullfils 1. and 2.; we say there is + an equivalent method in the packages quaternions_oo. + + If additonally the method y in the quaternions_oo package has the same name, + then we say that the method x exists in the package. + +The naming of the methods is not important, since the Robotics Toolbox for octave +will have a wrapper class quaternion. This class will emulate the API. + + +object.method(args) + +using the trick used here +[ http://octave.svn.sf.net/viewvc/octave/trunk/octave-forge/main/geometry/inst/io/%40svg/subsref.m?revision=8974&view=markup ] + += Marking convention = +In the [] field of each method/operator/property add + + e - There is an isomorphic method (equivalent). + x - There is an isomorphic method with the same name (exist). + * - There is an exact equal method in the package (same input, output and name). + b+ - Benchmarked, slower than current method in quaternions_oo. + b- - Benchmarked, faster than current + + c - There is a method with the same name but not isomorphic (conflict). + +Example 1: +A method qc = qconj(q) exist in quaternions_oo that calculates the inverse of a quaternion. +Then we mark inv as follows + + [e] inv + + - Example 2: + A method [h a] = dosomething(q) from in quaternions_oo to calculate something. + The method [h] = somethingtodo(q) from Robotics toolbox to calculate the same. + + [e] somethingtodo + + Since the first argument is the same. + The same holds ff [a h] = dosomething(q). Since we need just to swap output arguemnts. + + - Example 3: + A method [h] = dosomething(q) from in quaternions_oo to calculate something. + The method [h a] = somethingtodo(q) from Robotics toolbox to calculate the same. + + [ ] somethingtodo + + Since we need to check how to calculate the output a. + + - Example 4: + A method [h] = dosomething(q) from in quaternions_oo to calculate something. + The method [h a] = somethingtodo(q) from Robotics toolbox to calculate the same. + And you benchmarked the methods givin a positive result for the quaternions_oo. + + [b+] somethingtodo + + The b flag indicates that there is a point of comparision but the methods may not be equivalent. + + - Example 4: + A method [h] = dosomething(q) from in quaternions_oo to calculate something. + The method [h] = dosomething(q) from Robotics toolbox to calculate the same. + And you benchmarked the methods givin a positive result for the robotics toolbox. + + [*b-] dosomething + + just concatenate flags. + +We hope not to run into the c tag. + +== Quaternion == +DONE Q = Quaternion() is the identitity quaternion 1<0,0,0> representing a null rotation. + +DONE Q = Quaternion(Q1) is a copy of the quaternion Q1 + +DONE Q = Quaternion([S V1 V2 V3]) is a quaternion formed by specifying directly its 4 elements + +DONE Q = Quaternion(S) is a quaternion formed from the scalar S and zero vector part: S<0,0,0> + +DONE Q = Quaternion(V) is a pure quaternion with the specified vector part: 0<V> + +DONE Q = Quaternion(TH, V) is a unit quaternion corresponding to rotation of TH about the vector V. + +DONE Q = Quaternion(R) is a unit quaternion corresponding to the orthonormal rotation matrix R. + +DONE Q = Quaternion(T) is a unit quaternion equivalent to the rotational + += methods = +DONE [c] inv return inverse of quaterion +DONE [e] norm: Wraps abs from quaternions_oo +DONE [x] dot derivative of quaternion with angular velocity w +DONE [c] display +DONE [] q2tr +DONE [*] unit return unit quaternion + +[] plot same options as trplot() +[] interp interpolation (slerp) between q and q2, 0<=s<=1 +[] scale interpolation (slerp) between identity and q, 0<=s<=1 + += Operators = +DONE [*] q+q2 return elementwise sum of quaternions +DONE [*] q-q2 return elementwise difference of quaternions +DONE [*] q*q2 return quaternion product +DONE [*] q/q2 return q*q2.inv + +[*] q*v rotate vector by quaternion, v is 3x1 +DONE [*] q^n return q to power n (real) + += Properties (read only)= +DONE [] s real part +DONE [] v vector part +DONE [] R 3x3 rotation matrix +DONE [] T 4x4 homogeneous transform matrix
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/demoml.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,10 @@ +q = rot2q ([0, 0, 1], pi/4) + +[vv, theta] = q2rot (q) + +x = quaternion (0, 1, 1, 0) % nicht normiert + % s x y z + +rx = q * x * conj (q) % q x q^-1 + +[vv, theta] = q2rot (rx)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/generate_quaternion_pdf.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,12 @@ +homedir = pwd (); +develdir = fileparts (which ("generate_quaternion_pdf")); +pdfdir = [develdir, "/pdfdoc"]; +cd (pdfdir); + +collect_texinfo_strings + +for i = 1:5 + system ("pdftex -interaction batchmode quaternion.tex"); +endfor + +cd (homedir);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/makefile_quaternion.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,18 @@ +## ============================================================================== +## Developer Makefile for OCT-files +## ============================================================================== +## USAGE: * fetch quaternion_oo from Octave-Forge by svn +## * add quaternion_oo/inst, quaternion_oo/src and quaternion_oo/devel +## to your Octave path +## * run makefile_quaternion +## ============================================================================== + +homedir = pwd (); +develdir = fileparts (which ("makefile_quaternion")); +srcdir = [develdir, "/../src"]; +cd (srcdir); + +mkoctfile is_real_array.cc + +system ("rm *.o"); +cd (homedir); \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/pdfdoc/collect_texinfo_strings.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,41 @@ +% pack_name = "generate_html" +% pack_name = "control" +pack_name = "quaternion" + + +% Load Packages +pkg load "generate_html" +pkg ("load", pack_name); + +% Get list of functions +list = pkg ("describe", pack_name); + +%list + +% Open output file +fid = fopen ("functions.texi", "w"); + +for k = 1:numel (list {1}.provides) + + group = list {1}.provides{k}; + functions = group.functions; + + % fprintf (fid, '@section %s\n', group.category); + fprintf (fid, '@chapter %s\n', group.category); + + for k=1:numel(functions) + [TEXT, FORMAT] = get_help_text (functions(k)); + fun = functions{k}; + if (fun(1) == "@") + % fprintf (fid, '@subsection @%s\n', fun); + fprintf (fid, '@section @%s\n', fun); + else + % fprintf (fid, '@subsection %s\n', fun); + fprintf (fid, '@section %s\n', fun); + endif + fprintf (fid,TEXT); + end + +end + +fclose(fid);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/pdfdoc/info_generate_manual.txt Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,13 @@ +* Check that "pkg list" lists the packages generate_html and quaternion. +* Run collect_texinfo_strings within Octave. This script collects the Texinfo strings from all + functions listed in the package's INDEX file and writes them to the file functions.texi. + Don't edit the file functions.texi since your changes will be lost by the next run. +* Adapt version number in quaternion.tex +* Run quaternion.tex + + +pdftex quaternion.tex +q + +Alternatively: +Run generate_quaternion_pdf
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/pdfdoc/quaternion.tex Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,71 @@ +\input texinfo @c -*-texinfo-*- +@c %**start of header +@setfilename quaternion.info +@settitle Octave Quaternion Package +@afourpaper +@set VERSION 2.0.0 +@finalout +@c @afourwide +@c %**end of header + +@c %*** Start of TITLEPAGE +@titlepage +@title quaternion @value{VERSION} +@subtitle Quaternion Package for GNU Octave +@author Lukas F. Reichlin +@author Juan Pablo Carbajal +@page +@vskip 0pt plus 1filll +Copyright @copyright{} 2010-2012, Lukas F. Reichlin @email{lukas.reichlin@@gmail.com} + +This manual is generated automatically from the texinfo help strings +of the package's functions. + +Permission is granted to make and distribute verbatim copies of +this manual provided the copyright notice and this permission notice +are preserved on all copies. + +Permission is granted to copy and distribute modified versions of this +manual under the conditions for verbatim copying, provided that the entire +resulting derived work is distributed under the terms of a permission +notice identical to this one. + +Permission is granted to copy and distribute translations of this manual +into another language, under the same conditions as for modified versions. +@page +@chapheading Preface +The @acronym{GNU} Octave quaternion package from version 2 onwards +was developed by Lukas F. Reichlin with important contributions by +Juan Pablo Carbajal. This new package is intended as a replacement +for quaternion-1.0.0 by A. Scottedward Hodel. It is loosely based +on ideas from the Quaternion Toolbox for Matlab by Steve Sangwine +and Nicolas Le Bihan with a special focus on code simplicity and +vectorization. Its main features are: +@itemize +@item Matrices and n-dimensional arrays of quaternions. +@item Overloaded operators due to the use of classes introduced with Octave 3.2. +@item Operator semantics similar to Octave's built-in complex numbers. +@item Fully vectorized code for crunching large quaternion arrays in a speedy manner. +@end itemize + + +@sp 5 +@subheading Using the help function +Some functions of the quaternion package are listed with a leading @code{@@quaternion/}. +This is only needed to view the help text of the function, e.g. @w{@code{help norm}} +shows the built-in function while @w{@code{help @@quaternion/norm}} shows the overloaded +function for quaternions. Note that there are quaternion functions +like @code{unit} that have no built-in equivalent. + +When just using the function, the leading @code{@@quaternion/} must @strong{not} be typed. +Octave selects the right function automatically. So one can type @w{@code{norm (q)}} +and @w{@code{norm (matrix)}} regardless of the class of the argument. +@end titlepage +@c %*** End of TITLEPAGE + +@contents +@c @chapter Function Reference +@include functions.texi + +@end +@bye
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/q0.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,9 @@ +function q = q0 + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (1, 0, 0, 0); + +endfunction \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/q1.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,9 @@ +function q = q1 + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (0, 1, 0, 0); + +endfunction \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/q2.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,9 @@ +function q = q2 + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (0, 0, 1, 0); + +endfunction \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/q3.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,9 @@ +function q = q3 + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (0, 0, 0, 1); + +endfunction \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/q4.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,9 @@ +function q = q4 + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (1, 0, 0, 0); + +endfunction \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/q_2x2.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,10 @@ +w = [2, 6; 10, 14]; + +x = [3, 7; 11, 15]; + +y = [4, 8; 12, 16]; + +z = [5, 9; 13, 17]; + +q = quaternion (w, x, y, z) +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/q_2x3.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,10 @@ +w = [2, 6, 10; 14, 18, 22]; + +x = [3, 7, 11; 15, 19, 23]; + +y = [4, 8, 12; 16, 20, 24]; + +z = [5, 9, 13; 17, 21, 25]; + +q = quaternion (w, x, y, z) +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/qbug.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,3 @@ +q = quaternion (2, 3, 4, 5) + +diag ([q, q, q]) \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/quaternion.ps Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,8786 @@ +%!PS (but not EPSF; comments have been disabled) +%DVIPSCommandLine: dvips tmp -o quaternion.ps +%DVIPSParameters: dpi=600, compressed, comments removed +%DVIPSSource: TeX output 1998.10.23:1515 +/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N +/X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 +mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} +ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale +isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div +hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul +TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} +forall round exch round exch]setmatrix}N /@landscape{/isls true N}B +/@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B +/FMat[1 0 0 -1 0 0]N /FBB[0 0 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+5122 y Fi(h)895 5216 y Fo(I)g Fq(\(2)p Fo(q)1066 5179 +y Fk(2)1063 5239 y(4)1127 5216 y Fl(\000)20 b Fq(1\))h(+)f(2)7 +b(\026)-52 b Fo(q)10 b Fq(\026)-52 b Fo(q)1543 5179 y +Fh(T)1618 5216 y Fq(+)20 b(2\()7 b(\026)-52 b Fo(q)24 +b Fl(\002)c Fo(I)7 b Fq(\))p Fo(q)2068 5230 y Fk(4)2107 +5122 y Fi(i)2161 5216 y Fo(x)702 5384 y Fq(=)83 b(\(2)p +Fo(q)980 5347 y Fk(2)977 5407 y(4)1040 5384 y Fl(\000)20 +b Fq(1\))p Fo(x)h Fq(+)f(2)7 b(\026)-52 b Fo(q)10 b Fq(\026)-51 +b Fo(q)1509 5347 y Fh(T)1563 5384 y Fo(x)21 b Fq(+)f(2)p +Fo(q)1813 5398 y Fk(4)1852 5384 y Fq(\()7 b(\026)-52 +b Fo(q)23 b Fl(\002)d Fo(x)p Fq(\))p eop +8 7 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)g(Quaternions)f(\(In)m(tro)s +(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p Fo(:)p Fq(1)439 +b Fn(\(c\))32 b(1998)908 b Fq(8)0 399 y Fr(Remark)34 +b(1.4)46 b Fq(The)32 b(ab)s(o)m(v)m(e)i(deriv)-5 b(ation)31 +b(treats)i(a)f(quaternion)g(as)g(a)h(transformation)e(up)s(on)g(a)i(v)m +(ector)g(within)0 511 y(a)f(linear)d(space.)44 b(An)31 +b(alternativ)m(e)h(con)m(v)m(en)m(tion)g(is)f(used)f(in)g([R)-10 +b(W91)r(],)31 b(in)f(whic)m(h)g(the)i(quaternion)e(is)g(treated)j(as)0 +624 y(a)e(transformation)e(up)s(on)g(the)h(basis)g(v)m(ectors)h(of)g(a) +f(frame.)41 b(The)30 b(latter)g(con)m(v)m(en)m(tion)i(results)d(in)g(a) +i(sign)e(c)m(hange)0 737 y(of)i(the)f(angle)g(of)h(rotation,)g(i.e.,) +1150 941 y Fo(x)1202 955 y Fh(r)1323 941 y Fq(=)83 b(\(2)p +Fo(q)1601 904 y Fk(2)1598 964 y(4)1661 941 y Fl(\000)20 +b Fq(1\))p Fo(x)h Fq(+)f(2)7 b(\026)-52 b Fo(q)10 b Fq(\026)-52 +b Fo(q)2129 904 y Fh(T)2184 941 y Fo(x)20 b Fq(+)g(2)p +Fo(q)2433 955 y Fk(4)2472 941 y Fq(\()7 b(\026)-52 b +Fo(q)24 b Fl(\002)c Fo(x)p Fq(\))0 1146 y(Use)29 b(of)g(the)f(latter)h +(con)m(v)m(en)m(tion)h(results)d(in)g(a)i(similar)d(c)m(hange)k(in)d +(sign)h(in)f(the)i(time)f(deriv)-5 b(ativ)m(e)28 b(of)h(the)f(quater-)0 +1259 y(nion,)h(discussed)g(in)g(1.5.)0 1471 y Fr(M-\014le)46 +b Fj(qtransv)28 b Fq(Rotate)k(a)f(v)m(ector)227 1696 +y Fj(qtransv)46 b(is)h(the)g(function)f(defined)g(from:)g +(/home3/hodel/oct/quat/qt)o(rans)o(v.m)275 1922 y(vr)h(=)h +(qtransv\(vv,qr\))275 2035 y(rotate)e(a)i(3-vector)d(as)i(specified)f +(by)h(quaternion)e(qr)275 2148 y(q)i(=)h(\(ee,th\))93 +b(\(vector,)46 b(angle)g(notation\))275 2261 y(vr)h(=)h(\(vv)f(.)g +(ee\)*ee)f([projection)f(on)i(ee)g(unchanged)e(])514 +2374 y(+)i([vv)g(-)g(\(vv)g(.)h(ee\)*ee])e(cos\(th\))93 +b([what's)46 b(left)h(gets)f(scaled)g(by)i(cosine])514 +2487 y(+)f(\(vv)g(x)g(ee\))g(sin\(th\))571 b([and)47 +b(the)g(sine)f(term)h(completes)e(the)i(rotation])0 2711 +y Fr(M-\014le)f Fj(qtransvmat)57 b Fq(Obtain)30 b(3)20 +b Fl(\002)g Fq(3)31 b(rotation)g(matrix)e(from)h(a)h(quaternion)275 +2936 y Fj([xv,yv,zv])45 b(=)i(qtransvmat\(q\))275 3049 +y(xm)g(=)h(qtransvmat\(q\),)c(xm)j(=)g([xv)g(yv)g(zv])275 +3162 y(compute)f(x,y,z)g(axes)h(rotated)f(per)h(specified)e(quaternion) +g(q)0 3387 y Fr(Example)34 b(1.4)46 b Fq(Use)30 b(of)h(quaternions)e +(to)i(view)f(b)s(o)s(dy/inertial)d(frame)k(transformations:)0 +3575 y Fj(degrees)46 b(=)h(pi/180;)189 b(daz)47 b(=)h(30*degrees;)188 +b(del)46 b(=)i(-20*degrees;)0 3688 y(qazimuth)e(=)h +(quaternion\([0,0,1],daz\);)0 3801 y(qelevation)e(=)i +(quaternion\([cos\(daz\),sin\(d)o(az\),)o(0],)o(del\))o(;)0 +3914 y(qview)f(=)i(qmult\(qelevation,qazimut)o(h\);)0 +4139 y(th)f(=)h(0:5:20;)0 4252 y(ov)f(=)h(ones\(size\(th\)\);)0 +4365 y(myth)f(=)g([th,max\(th\)*ov)d(;)j(0*ov,th];)0 +4478 y(myth)g(=)g([[0:5:20])e(,)j(20*ones\(1,4\),20*ones\(1,4)o(\);)41 +b(...)382 4591 y(zeros\(1,5\),)k(5:5:20,)g(20*ones\(1,4\);)g(...)382 +4704 y(zeros\(1,5\),)g(zeros\(1,4\),)f([5:5:20]];)0 4930 +y(#)j(inertial)f(frame)g(quaternion)0 5043 y(qin)h(=)g(quaternion\([1)e +(0)i(0],180*degrees\);)0 5156 y(for)g(kk=1:length\(myth\(1,:\)\))95 +5269 y(figure\(kk\))95 5381 y(thy)g(=)h(myth\(1,kk\);)140 +b(thp)47 b(=)g(myth\(2,kk\);)141 b(thr)46 b(=)i(myth\(3,kk\);)p +eop +9 8 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)436 b Fn(\(c\))31 b(1998)902 b Fq(9)95 399 +y Fj(#)48 b(avoid)e(transformations)e(by)j(reversing)e(the)i(order)g +(of)g(multiplication!)95 511 y(qyi)g(=)h(quaternion\([0,0,1],thy*d)o +(egr)o(ees\))o(;)95 624 y(qp1)f(=)h(quaternion\([0,1,0],thp*d)o(egr)o +(ees\))o(;)95 737 y(qr2)f(=)h(quaternion\([1,0,0],thr*d)o(egr)o(ees\))o +(;)95 850 y(qbi)f(=)h(qmult\(qyi,qmult\(qp1,qr2\))o(\);)95 +1076 y(printf\("yaw=\0458.4f,)43 b(pitch=\0458.4f,)i(\\n)190 +b(qbi)47 b(=)g(\(\0458.4f\)i)f(+)h(\(\0458.4e\)j)f(+)h(\(\0458.4f\)k)f +(+)h(\()0 1189 y(\0458.4f\)\\n",thy,thp,)c(...)382 1302 +y(qbi\(1\),)j(qbi\(2\),)f(qbi\(3\),)h(qbi\(4\)\);)95 +1415 y([vv,th])g(=)i(quaternion\(qbi\);)95 1528 y(printf\(")285 +b(=)47 b(\(vector\))f(=)h([\0458.4f)f(\0458.4f)h(\0458.4f],)e +(th=\0455.2f)h(deg\\n",)g(...)382 1641 y(vv\(1\),)g(vv\(2\),)g +(vv\(3\),)g(th*180/pi\);)95 1866 y(#)i(transform)d(qbi)i(to)g +(reference)f(coordinates)95 1979 y(qb)i(=)f(qmult\(qin,qbi\);)95 +2092 y(title\(sprintf\("yaw=\0455.2f,)41 b(pitch=\0455.2f,)k +(roll=\0455.2f)g(\(deg\)",thy,thp,thr\)\))95 2205 y +(coordinate_plot\(qin,qb,qvi)o(ew\);)95 2318 y(gset)i(terminal)f +(postscript)f(eps)95 2431 y(eval\(sprintf\("gset)e(output)j +('fig\045d.eps'",kk\)\);)95 2544 y(replot)95 2657 y(gset)h(terminal)f +(x11)0 2770 y(endfor)0 2957 y Fq(Results:)316 2924 y +Fk(1)50 4816 y @beginspecial 50 @llx 50 @lly 410 @urx +302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 0.00 deg) Cshow +2737 4900 M +(reference coordinates) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +2252 2272 L +2737 2625 Pls +2252 2272 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +-177 970 V +2737 2625 Crs +2560 3595 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +2252 2272 L +2737 2625 Star +2252 2272 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +-177 970 V +2737 2625 Box +2560 3595 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-177 970 V +-89 0 V +1.000 UL +LT3 +3323 1302 M +-1789 0 V +1181 3242 L +970 706 V +1789 0 V +4293 2008 L +3323 1302 L +970 706 V +-1788 0 V +2151 3948 L +2505 2008 L +1534 1302 L +1.000 UL +LT4 +3940 3948 M +2969 3242 L +-1788 0 V +1788 0 V +3323 1302 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 0.00 deg) Cshow +2737 4900 M +(yaw= 0.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Pls +3369 3141 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +-73 0 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 0 4911 1560 4 v 104 4965 a Fe(1)138 4997 +y Fc(due)28 b(to)g(details)h(of)g(visualization)h(soft)n(w)n(are,)h +(the)d Fb(x)18 b Fa(\000)g Fb(y)j Fa(\000)e Fb(z)31 b +Fc(axes)d(do)g(not)g(app)r(ear)h(as)g(a)f(righ)n(t-handed)f(co)r +(ordinate)j(system.)0 5088 y(Sorry)-6 b(.)p eop +10 9 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(10)50 2045 +y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 +@rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 5.00 deg) Cshow +2737 4900 M +(yaw= 5.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3409 2580 M +-672 45 V +3409 2580 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +693 514 V +2737 2625 Pls +3430 3139 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +78 5 V +10 10 V +6 10 V +3 9 V +-3 7 V +-6 6 V +-10 3 V +-14 2 V +-16 -1 V +-18 -3 V +-20 -6 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 10.00 deg) Cshow +2737 4900 M +(yaw=10.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3346 2535 M +-609 90 V +3346 2535 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +749 508 V +2737 2625 Pls +3486 3133 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +83 9 V +8 11 V +5 9 V +0 8 V +-4 7 V +-8 5 V +-11 2 V +-15 1 V +-17 -2 V +-19 -4 V +-21 -6 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly +410 @urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 15.00 deg) Cshow +2737 4900 M +(yaw=15.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3279 2491 M +-542 134 V +3279 2491 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +800 499 V +2737 2625 Pls +3537 3124 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +87 14 V +7 10 V +2 9 V +-1 7 V +-6 6 V +-9 4 V +-13 2 V +-16 -1 V +-18 -3 V +-20 -5 V +-20 -6 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 20.00 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3207 2448 M +-470 177 V +3207 2448 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +90 18 V +5 10 V +1 8 V +-3 7 V +-7 5 V +-11 3 V +-14 1 V +-17 -2 V +-19 -3 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial eop +11 10 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(11)50 2045 +y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 +@rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 20.00 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch= 0.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3207 2448 M +-470 177 V +3207 2448 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Crs +3102 1731 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-365 894 V +90 18 V +5 10 V +1 8 V +-3 7 V +-7 5 V +-11 3 V +-14 1 V +-17 -2 V +-19 -3 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 20.61 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch= 5.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3173 2527 M +-436 98 V +3173 2527 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +405 -906 V +2737 2625 Crs +3142 1719 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-375 886 V +90 18 V +5 10 V +1 9 V +-3 7 V +-7 5 V +-11 3 V +-15 1 V +-17 -1 V +-18 -4 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly +410 @urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 22.34 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch=10.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3136 2606 M +-399 19 V +3136 2606 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +441 -911 V +2737 2625 Crs +3178 1714 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-384 878 V +89 18 V +6 11 V +0 9 V +-3 7 V +-7 5 V +-11 3 V +-15 1 V +-16 -1 V +-19 -4 V +-20 -6 V +-20 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 24.95 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch=15.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3096 2686 M +-359 -61 V +3096 2686 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +474 -909 V +2737 2625 Crs +3211 1716 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-394 870 V +90 18 V +5 11 V +1 9 V +-4 8 V +-7 5 V +-11 3 V +-14 1 V +-17 -1 V +-19 -4 V +-20 -6 V +-19 -8 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial eop +12 11 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 +b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p +Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(12)50 2045 +y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 +@rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 28.21 deg) Cshow +2737 4900 M +(yaw=20.00 deg, pitch=20.00 deg) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3054 2765 M +2737 2625 L +3054 2765 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +844 485 V +2737 2625 Pls +3581 3110 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +504 -901 V +2737 2625 Crs +3241 1724 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3467 2625 M +-730 0 V +3467 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +632 516 V +2737 2625 Star +3369 3141 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +365 -894 V +2737 2625 Box +3102 1731 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-403 861 V +89 19 V +5 11 V +1 10 V +-3 7 V +-7 6 V +-11 3 V +-15 1 V +-16 -1 V +-19 -4 V +-20 -6 V +-19 -9 V +1.000 UL +LT3 +3200 1215 M +-1460 0 V +1010 3003 L +2274 4035 L +1460 0 V +4464 2247 L +3200 1215 L +4464 2247 L +-1460 0 V +2274 4035 L +3004 2247 L +1740 1215 L +1.000 UL +LT4 +3734 4035 M +2470 3003 L +-1460 0 V +1460 0 V +3200 1215 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 28.71 deg) Cshow +2737 4900 M +(yaw=20.00, pitch=20.00, roll=10.00 \(deg\)) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3622 3070 M +2737 2625 L +3622 3070 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +236 176 V +2737 2625 Pls +2973 2801 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +476 -915 V +2737 2625 Crs +3213 1710 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +485 353 V +2737 2625 Star +3222 2978 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +177 -970 V +2737 2625 Box +2914 1655 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-140 990 V +100 8 V +2 6 V +-2 5 V +-7 4 V +-11 3 V +-14 2 V +-18 1 V +-19 0 V +-21 -2 V +-22 -3 V +-21 -4 V +1.000 UL +LT3 +3323 1302 M +-1789 0 V +1181 3242 L +970 706 V +1789 0 V +4293 2008 L +3323 1302 L +970 706 V +-1788 0 V +2151 3948 L +2505 2008 L +1534 1302 L +1.000 UL +LT4 +3940 3948 M +2969 3242 L +-1788 0 V +1788 0 V +3323 1302 L +stroke +grestore +end +showpage + @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly +410 @urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +end +gnudict begin +gsave +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 140 scalefont setfont +LTb +672 560 M +63 0 V +4067 0 R +-63 0 V +588 560 M +(-2) Rshow +672 1076 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1.5) Rshow +672 1593 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-1) Rshow +672 2109 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(-0.5) Rshow +672 2625 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0) Rshow +672 3141 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(0.5) Rshow +672 3658 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1) Rshow +672 4174 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(1.5) Rshow +672 4690 M +63 0 V +4067 0 R +-63 0 V +-4151 0 R +(2) Rshow +672 560 M +0 63 V +0 4067 R +0 -63 V +672 420 M +(-2) Cshow +1188 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1.5) Cshow +1705 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-1) Cshow +2221 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(-0.5) Cshow +2737 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0) Cshow +3253 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(0.5) Cshow +3770 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1) Cshow +4286 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(1.5) Cshow +4802 560 M +0 63 V +0 4067 R +0 -63 V +0 -4207 R +(2) Cshow +LTb +672 560 M +4130 0 V +0 4130 V +-4130 0 V +672 560 L +2737 210 M +(rotate about eigenaxis 30.19 deg) Cshow +2737 4900 M +(yaw=20.00, pitch=20.00, roll=15.00 \(deg\)) Cshow +1.000 UP +1.000 UL +LT0 +4151 4557 M +(x \(body\)) Rshow +4235 4557 M +399 0 V +3622 3070 M +2737 2625 L +3622 3070 Pls +2737 2625 Pls +4434 4557 Pls +1.000 UP +1.000 UL +LT1 +4151 4417 M +(y \(body\)) Rshow +4235 4417 M +399 0 V +2737 2625 M +277 95 V +2737 2625 Pls +3014 2720 Pls +4434 4417 Pls +1.000 UP +1.000 UL +LT2 +4151 4277 M +(z \(body\)) Rshow +4235 4277 M +399 0 V +2737 2625 M +454 -927 V +2737 2625 Crs +3191 1698 Crs +4434 4277 Crs +1.000 UP +1.000 UL +LT0 +4151 4137 M +(x \(inertial\)) Rshow +4235 4137 M +399 0 V +3631 2625 M +-894 0 V +3631 2625 Star +2737 2625 Star +4434 4137 Star +1.000 UP +1.000 UL +LT1 +4151 3997 M +(y \(inertial\)) Rshow +4235 3997 M +399 0 V +2737 2625 M +485 353 V +2737 2625 Star +3222 2978 Star +4434 3997 Star +1.000 UP +1.000 UL +LT2 +4151 3857 M +(z \(inertial\)) Rshow +4235 3857 M +399 0 V +2737 2625 M +177 -970 V +2737 2625 Box +2914 1655 Box +4434 3857 Box +1.000 UL +LT5 +4151 3717 M +(eigenaxis) Rshow +4235 3717 M +399 0 V +2737 2625 M +-129 990 V +100 6 V +3 6 V +-2 5 V +-7 5 V +-10 3 V +-15 3 V +-17 1 V +-19 0 V +-21 -1 V +-22 -3 V +-21 -4 V +1.000 UL +LT3 +3323 1302 M +-1789 0 V +1181 3242 L +970 706 V +1789 0 V +4293 2008 L +3323 1302 L +970 706 V +-1788 0 V +2151 3948 L +2505 2008 L +1534 1302 L +1.000 UL +LT4 +3940 3948 M +2969 3242 L +-1788 0 V +1788 0 V +3323 1302 L +stroke +grestore +end +showpage + @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 +@urx 302 @ury 2808 @rwi @setspecial +/gnudict 120 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke gnulinewidth 2 mul setlinewidth } def +/AL { stroke gnulinewidth 2 div setlinewidth } def +/UL { gnulinewidth mul /userlinewidth exch def } def +/PL { stroke userlinewidth setlinewidth } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 0 1 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def +/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V 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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/devel/quaternion_arrays.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,58 @@ +i = ones (3, 3); + +w = 2*i; +x = 3*i; +y = 4*i; +z = 5*i; + +q = quaternion (w, x, y, z) + +q .* conj (q) + + +%{ + +octave:1> quaternion_matrices +q.w = + 2 2 2 + 2 2 2 + 2 2 2 + +q.x = + 3 3 3 + 3 3 3 + 3 3 3 + +q.y = + 4 4 4 + 4 4 4 + 4 4 4 + +q.z = + 5 5 5 + 5 5 5 + 5 5 5 + +ans.w = + 54 54 54 + 54 54 54 + 54 54 54 + +ans.x = + 0 0 0 + 0 0 0 + 0 0 0 + +ans.y = + 0 0 0 + 0 0 0 + 0 0 0 + +ans.z = + 0 0 0 + 0 0 0 + 0 0 0 + +octave:2> + +%} \ No newline at end of file
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vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 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2625 M -2252 2272 L -2737 2625 Pls -2252 2272 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M --177 970 V -2737 2625 Crs -2560 3595 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3631 2625 M --894 0 V -3631 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -2252 2272 L -2737 2625 Star -2252 2272 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M --177 970 V -2737 2625 Box -2560 3595 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --177 970 V --89 0 V -1.000 UL -LT3 -3323 1302 M --1789 0 V -1181 3242 L -970 706 V -1789 0 V -4293 2008 L -3323 1302 L -970 706 V --1788 0 V -2151 3948 L -2505 2008 L -1534 1302 L -1.000 UL -LT4 -3940 3948 M -2969 3242 L --1788 0 V -1788 0 V -3323 1302 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict 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a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 -b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p -Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(10)50 2045 -y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 -@rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 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Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -78 5 V -10 10 V -6 10 V -3 9 V --3 7 V --6 6 V --10 3 V --14 2 V --16 -1 V --18 -3 V --20 -6 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 10.00 deg) Cshow -2737 4900 M -(yaw=10.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3346 2535 M --609 90 V -3346 2535 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -749 508 V -2737 2625 Pls -3486 3133 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -83 9 V -8 11 V -5 9 V -0 8 V --4 7 V --8 5 V --11 2 V --15 1 V --17 -2 V --19 -4 V --21 -6 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly -410 @urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 15.00 deg) Cshow -2737 4900 M -(yaw=15.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3279 2491 M --542 134 V -3279 2491 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -800 499 V -2737 2625 Pls -3537 3124 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -87 14 V -7 10 V -2 9 V --1 7 V --6 6 V --9 4 V --13 2 V --16 -1 V --18 -3 V --20 -5 V --20 -6 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 20.00 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3207 2448 M --470 177 V -3207 2448 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -90 18 V -5 10 V -1 8 V --3 7 V --7 5 V --11 3 V --14 1 V --17 -2 V --19 -3 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial eop -11 10 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 -b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p -Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(11)50 2045 -y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 -@rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 20.00 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch= 0.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3207 2448 M --470 177 V -3207 2448 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Crs -3102 1731 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --365 894 V -90 18 V -5 10 V -1 8 V --3 7 V --7 5 V --11 3 V --14 1 V --17 -2 V --19 -3 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 20.61 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch= 5.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3173 2527 M --436 98 V -3173 2527 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -405 -906 V -2737 2625 Crs -3142 1719 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --375 886 V -90 18 V -5 10 V -1 9 V --3 7 V --7 5 V --11 3 V --15 1 V --17 -1 V --18 -4 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly -410 @urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 22.34 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch=10.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3136 2606 M --399 19 V -3136 2606 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -441 -911 V -2737 2625 Crs -3178 1714 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --384 878 V -89 18 V -6 11 V -0 9 V --3 7 V --7 5 V --11 3 V --15 1 V --16 -1 V --19 -4 V --20 -6 V --20 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 24.95 deg) Cshow -2737 4900 M -(yaw=20.00 deg, pitch=15.00 deg) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3096 2686 M --359 -61 V -3096 2686 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -844 485 V -2737 2625 Pls -3581 3110 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -474 -909 V -2737 2625 Crs -3211 1716 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --394 870 V -90 18 V -5 11 V -1 9 V --4 8 V --7 5 V --11 3 V --14 1 V --17 -1 V --19 -4 V --20 -6 V --19 -8 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial eop -12 11 bop 0 100 a Fn(A.)31 b(S.)f(Ho)s(del:)40 b(Quaternions)29 -b(\(In)m(tro)s(duction\))g Fo(R)q(ev)s(ision)d Fq(:)f(1)p -Fo(:)p Fq(1)421 b Fn(\(c\))31 b(1998)871 b Fq(12)50 2045 -y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2808 -@rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M 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\(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -504 -901 V -2737 2625 Crs -3241 1724 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3467 2625 M --730 0 V -3467 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -632 516 V -2737 2625 Star -3369 3141 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -365 -894 V -2737 2625 Box -3102 1731 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --403 861 V -89 19 V -5 11 V -1 10 V --3 7 V --7 6 V --11 3 V --15 1 V --16 -1 V --19 -4 V --20 -6 V --19 -9 V -1.000 UL -LT3 -3200 1215 M --1460 0 V -1010 3003 L -2274 4035 L -1460 0 V -4464 2247 L -3200 1215 L -4464 2247 L --1460 0 V -2274 4035 L -3004 2247 L -1740 1215 L -1.000 UL -LT4 -3734 4035 M -2470 3003 L --1460 0 V -1460 0 V -3200 1215 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 28.71 deg) Cshow -2737 4900 M -(yaw=20.00, pitch=20.00, roll=10.00 \(deg\)) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3622 3070 M -2737 2625 L -3622 3070 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -236 176 V -2737 2625 Pls -2973 2801 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -476 -915 V -2737 2625 Crs -3213 1710 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3631 2625 M --894 0 V -3631 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -485 353 V -2737 2625 Star -3222 2978 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -177 -970 V -2737 2625 Box -2914 1655 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --140 990 V -100 8 V -2 6 V --2 5 V --7 4 V --11 3 V --14 2 V --18 1 V --19 0 V --21 -2 V --22 -3 V --21 -4 V -1.000 UL -LT3 -3323 1302 M --1789 0 V -1181 3242 L -970 706 V -1789 0 V -4293 2008 L -3323 1302 L -970 706 V --1788 0 V -2151 3948 L -2505 2008 L -1534 1302 L -1.000 UL -LT4 -3940 3948 M -2969 3242 L --1788 0 V -1788 0 V -3323 1302 L -stroke -grestore -end -showpage - @endspecial 50 3833 a @beginspecial 50 @llx 50 @lly -410 @urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def -/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def -/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def -/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def -/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def -/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def -/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def -/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def -/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def -/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def -/DiaE { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke } def -/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke } def -/TriUE { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke } def -/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke } def -/PentE { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore } def -/CircE { stroke [] 0 setdash - hpt 0 360 arc stroke } def -/BoxFill { gsave Rec 1 setgray fill grestore } def -end -gnudict begin -gsave -50 50 translate -0.050 0.050 scale -0 setgray -newpath -(Helvetica) findfont 140 scalefont setfont -LTb -672 560 M -63 0 V -4067 0 R --63 0 V -588 560 M -(-2) Rshow -672 1076 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1.5) Rshow -672 1593 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-1) Rshow -672 2109 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(-0.5) Rshow -672 2625 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0) Rshow -672 3141 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(0.5) Rshow -672 3658 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1) Rshow -672 4174 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(1.5) Rshow -672 4690 M -63 0 V -4067 0 R --63 0 V --4151 0 R -(2) Rshow -672 560 M -0 63 V -0 4067 R -0 -63 V -672 420 M -(-2) Cshow -1188 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1.5) Cshow -1705 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-1) Cshow -2221 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(-0.5) Cshow -2737 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0) Cshow -3253 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(0.5) Cshow -3770 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1) Cshow -4286 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(1.5) Cshow -4802 560 M -0 63 V -0 4067 R -0 -63 V -0 -4207 R -(2) Cshow -LTb -672 560 M -4130 0 V -0 4130 V --4130 0 V -672 560 L -2737 210 M -(rotate about eigenaxis 30.19 deg) Cshow -2737 4900 M -(yaw=20.00, pitch=20.00, roll=15.00 \(deg\)) Cshow -1.000 UP -1.000 UL -LT0 -4151 4557 M -(x \(body\)) Rshow -4235 4557 M -399 0 V -3622 3070 M -2737 2625 L -3622 3070 Pls -2737 2625 Pls -4434 4557 Pls -1.000 UP -1.000 UL -LT1 -4151 4417 M -(y \(body\)) Rshow -4235 4417 M -399 0 V -2737 2625 M -277 95 V -2737 2625 Pls -3014 2720 Pls -4434 4417 Pls -1.000 UP -1.000 UL -LT2 -4151 4277 M -(z \(body\)) Rshow -4235 4277 M -399 0 V -2737 2625 M -454 -927 V -2737 2625 Crs -3191 1698 Crs -4434 4277 Crs -1.000 UP -1.000 UL -LT0 -4151 4137 M -(x \(inertial\)) Rshow -4235 4137 M -399 0 V -3631 2625 M --894 0 V -3631 2625 Star -2737 2625 Star -4434 4137 Star -1.000 UP -1.000 UL -LT1 -4151 3997 M -(y \(inertial\)) Rshow -4235 3997 M -399 0 V -2737 2625 M -485 353 V -2737 2625 Star -3222 2978 Star -4434 3997 Star -1.000 UP -1.000 UL -LT2 -4151 3857 M -(z \(inertial\)) Rshow -4235 3857 M -399 0 V -2737 2625 M -177 -970 V -2737 2625 Box -2914 1655 Box -4434 3857 Box -1.000 UL -LT5 -4151 3717 M -(eigenaxis) Rshow -4235 3717 M -399 0 V -2737 2625 M --129 990 V -100 6 V -3 6 V --2 5 V --7 5 V --10 3 V --15 3 V --17 1 V --19 0 V --21 -1 V --22 -3 V --21 -4 V -1.000 UL -LT3 -3323 1302 M --1789 0 V -1181 3242 L -970 706 V -1789 0 V -4293 2008 L -3323 1302 L -970 706 V --1788 0 V -2151 3948 L -2505 2008 L -1534 1302 L -1.000 UL -LT4 -3940 3948 M -2969 3242 L --1788 0 V -1788 0 V -3323 1302 L -stroke -grestore -end -showpage - @endspecial 2050 w @beginspecial 50 @llx 50 @lly 410 -@urx 302 @ury 2808 @rwi @setspecial -/gnudict 120 dict def -gnudict begin -/Color false def -/Solid false def -/gnulinewidth 5.000 def -/userlinewidth gnulinewidth def -/vshift -46 def -/dl {10 mul} def -/hpt_ 31.5 def -/vpt_ 31.5 def -/hpt hpt_ def -/vpt vpt_ def -/M {moveto} bind def -/L {lineto} bind def -/R {rmoveto} bind def -/V {rlineto} bind def -/vpt2 vpt 2 mul def -/hpt2 hpt 2 mul def -/Lshow { currentpoint stroke M - 0 vshift R show } def -/Rshow { currentpoint stroke M - dup stringwidth pop neg vshift R show } def -/Cshow { currentpoint stroke M - dup stringwidth pop -2 div vshift R show } def -/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def - /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def -/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } - {pop pop pop Solid {pop []} if 0 setdash} ifelse } def -/BL { stroke gnulinewidth 2 mul setlinewidth } def -/AL { stroke gnulinewidth 2 div setlinewidth } def -/UL { gnulinewidth mul /userlinewidth exch def } def -/PL { stroke userlinewidth setlinewidth } def -/LTb { BL [] 0 0 0 DL } def -/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def -/LT0 { PL [] 0 1 0 DL } def -/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def -/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def -/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def -/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def -/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def -/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def -/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def -/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def -/Pnt { stroke [] 0 setdash - gsave 1 setlinecap M 0 0 V stroke grestore } def -/Dia { stroke [] 0 setdash 2 copy vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke - Pnt } def -/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V - currentpoint stroke M - hpt neg vpt neg R hpt2 0 V stroke - } def -/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke - Pnt } def -/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M - hpt2 vpt2 neg V currentpoint stroke M - hpt2 neg 0 R hpt2 vpt2 V stroke } def -/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke - Pnt } def -/Star { 2 copy Pls Crs } def -/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath fill } def -/TriUF { stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath fill } def -/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke - Pnt } def -/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath fill} def -/DiaF { stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath fill } def -/Pent { stroke [] 0 setdash 2 copy gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore Pnt } def -/PentF { stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath fill grestore } def -/Circle { stroke [] 0 setdash 2 copy - hpt 0 360 arc stroke Pnt } def -/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def -/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def -/C1 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - vpt 0 360 arc closepath } bind def -/C2 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C3 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C4 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C5 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc - 2 copy moveto - 2 copy vpt 180 270 arc closepath fill - vpt 0 360 arc } bind def -/C6 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C7 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 270 arc closepath fill - vpt 0 360 arc closepath } bind def -/C8 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C9 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath } bind def -/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath } bind def -/C11 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C12 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C13 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/C14 { BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc } bind def -/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath } bind def -/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath } bind def -/Square { dup Rec } bind def -/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def -/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def -/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def -/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def -/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def -/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill - Bsquare } bind def -/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def -/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def -/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare } bind def -/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare } bind def -/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def -/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare } bind def -/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def -/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def -/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def -/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def -/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def -/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def -/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def -/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def -/D6 { 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-y(quaternion,)30 b(3)0 1017 y(Euler)f(angles)166 1130 -y(quaternions,)g(6)0 1326 y(Octa)m(v)m(e)166 1439 y Fj(qinv)p -Fq(,)h(3)166 1552 y Fj(qmult)p Fq(,)f(3)166 1665 y Fj(qtrans)p -Fq(,)g(4)166 1778 y(qtransv,)h(8)166 1891 y(qtransvmat,)h(8)166 -2004 y Fj(quaternion)p Fq(,)d(2)0 2200 y(quaternions)166 -2313 y(as)j(co)s(ordinate)f(rotations,)h(3)166 2425 y(co)s(ordinate)f -(transformation,)g(4)166 2538 y(co)s(ordinate)g(transformation)g -(matrices,)h(6)166 2651 y(cross)g(pro)s(ducts,)e(2)166 -2764 y(de\014nition,)f(2)166 2877 y(deriv)-5 b(ativ)m(es,)30 -b(12)166 2990 y(Euler)f(angles,)h(6)166 3103 y(m)m(ultiplication,)e(2) -166 3216 y(unit)h(quaternions,)g(3)1905 5656 y(14)p eop -end -userdict /end-hook known{end-hook}if
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/abs.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,38 @@ +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{qabs} =} abs (@var{q}) +## Modulus of a quaternion. +## +## @example +## q = w + x*i + y*j + z*k +## abs (q) = sqrt (w.^2 + x.^2 + y.^2 + z.^2) +## @end example +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: August 2010 +## Version: 0.2 + +function b = abs (a) + + if (nargin != 1) + print_usage (); + endif + + b = sqrt (norm2 (a)); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/blkdiag.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,60 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{q} =} blkdiag (@var{q1}, @var{q2}, @dots{}) +## Block-diagonal concatenation of quaternions. +## @end deftypefn + + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: December 2011 +## Version: 0.1 + +function q = blkdiag (varargin) + + tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! + + w = blkdiag (tmp.w); + x = blkdiag (tmp.x); + y = blkdiag (tmp.y); + z = blkdiag (tmp.z); + + q = quaternion (w, x, y, z); + +endfunction + + +%!shared C, D +%! Aw = [2, 6; 10, 14]; +%! Ax = [3, 7; 11, 15]; +%! Ay = [4, 8; 12, 16]; +%! Az = [5, 9; 13, 17]; +%! A = quaternion (Aw, Ax, Ay, Az); +%! +%! Bw = [2, 6, 10; 14, 18, 22]; +%! Bx = [3, 7, 11; 15, 19, 23]; +%! By = [4, 8, 12; 16, 20, 24]; +%! Bz = [5, 9, 13; 17, 21, 25]; +%! B = quaternion (Bw, Bx, By, Bz); +%! +%! C = blkdiag (A, B); +%! +%! Dw = blkdiag (Aw, Bw); +%! Dx = blkdiag (Ax, Bx); +%! Dy = blkdiag (Ay, By); +%! Dz = blkdiag (Az, Bz); +%! D = quaternion (Dw, Dx, Dy, Dz); +%!assert (C == D);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/cat.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,36 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{q} =} cat (@var{dim}, @var{q1}, @var{q2}, @dots{}) +## Concatenation of quaternions along dimension @var{dim}. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function q = cat (dim, varargin) + + tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! + + w = cat (dim, tmp.w); + x = cat (dim, tmp.x); + y = cat (dim, tmp.y); + z = cat (dim, tmp.z); + + q = quaternion (w, x, y, z); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/columns.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,34 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{nc} =} columns (@var{q}) +## Return number of columns @var{nc} of quaternion array @var{q}. +## @end deftypefn + + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function c = columns (a) + + if (nargin != 1) + print_usage (); + endif + + c = columns (a.w); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/conj.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,40 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{q} =} conj (@var{q}) +## Return conjugate of a quaternion. +## +## @example +## q = w + x*i + y*j + z*k +## conj (q) = w - x*i - y*j - z*k +## @end example +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = conj (a) + + if (nargin != 1) + print_usage (); + endif + + a.x = -a.x; + a.y = -a.y; + a.z = -a.z; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/ctranspose.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,31 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Conjugate transpose of a quaternion. Used by Octave for "q'". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = ctranspose (a) + + if (nargin != 1) + print_usage (); + endif + + a = conj (transpose (a)); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/diag.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,53 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{q} =} diag (@var{v}) +## @deftypefnx {Function File} {@var{q} =} diag (@var{v}, @var{k}) +## Return a diagonal quaternion matrix with quaternion vector V on diagonal K. +## The second argument is optional. If it is positive, +## the vector is placed on the K-th super-diagonal. +## If it is negative, it is placed on the -K-th sub-diagonal. +## The default value of K is 0, and the vector is placed +## on the main diagonal. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = diag (a, b = 0) + + if (nargin == 0 || nargin > 2) + print_usage (); + endif + + a.w = diag (a.w, b); + a.x = diag (a.x, b); + a.y = diag (a.y, b); + a.z = diag (a.z, b); + +endfunction + + +%!shared R, S +%! Q = quaternion (2, 3, 4, 5); +%! R = diag ([Q, Q, Q]); +%! W = diag ([2, 2, 2]); +%! X = diag ([3, 3, 3]); +%! Y = diag ([4, 4, 4]); +%! Z = diag ([5, 5, 5]); +%! S = quaternion (W, X, Y, Z); +%!assert (R == S);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/diff.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,64 @@ +## Copyright (c) 1998, 2000, 2005, 2007 Auburn University. +## Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch> +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{qdot} =} diff (@var{q}, @var{omega}) +## Derivative of a quaternion. +## +## Let Q be a quaternion to transform a vector from a fixed frame to +## a rotating frame. If the rotating frame is rotating about the +## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative +## of Q is given by +## +## @example +## Q' = diff(Q, omega) +## @end example +## +## If the passive convention is used (rotate the frame, not the vector), +## then +## +## @example +## Q' = diff(Q,-omega) +## @end example +## @end deftypefn + +## Adapted from: qderiv by A. S. Hodel <a.s.hodel@eng.auburn.edu> + +function qd = diff (q, Omega) + + if (nargin != 2) + print_usage (); + endif + + if (! isa (q, "quaternion") || ! isscalar (q.w)) + error ("quaternion: first argument '%s' must be a scalar quaternion", inputname(1)); + endif + + Omega = vec (Omega); + + if (length (Omega) != 3) + error ("quaternion: second argument '%s' must be a length 3 vector", inputname(2)); + endif + + qd = 0.5 * quaternion (Omega(1), Omega(2), Omega(3)) * q; + +endfunction + +%!shared q +%! q = quaternion(3,1,0,0); + +%!assert(quaternion(0,0,0.5,1.5) == diff(q,[0 0 1])) +%!assert(quaternion(0,0,2,1) == diff(q,[0 1 1]))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/display.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,63 @@ +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Display routine for quaternions. Used by Octave internally. + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.2 + +function display (q) + + name = inputname(1); + s = size (q); + + if (length (s) == 2 && all (s == 1)) # scalar quaternion + w = num2str (q.w, 4); + x = __num2str__ (q.x); + y = __num2str__ (q.y); + z = __num2str__ (q.z); + disp ([name, " = ", w, x, "i" y, "j", z, "k"]); + disp (""); + else # non-scalar quaternion + disp ([name, ".w ="]); + disp (q.w); + disp (""); + disp ([name, ".x ="]); + disp (q.x); + disp (""); + disp ([name, ".y ="]); + disp (q.y); + disp (""); + disp ([name, ".z ="]); + disp (q.z); + disp (""); + endif + +endfunction + + +function str = __num2str__ (num) + + if (sign (num) == -1) + str = " - "; + else + str = " + "; + endif + + str = [str, num2str(abs (num), 4)]; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/eq.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,35 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Equal to operator for two quaternions. Used by Octave for "q1 == q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function flg = eq (a, b) + + if (! isa (a, "quaternion")) + a = quaternion (a); + endif + + if (! isa (b, "quaternion")) + b = quaternion (b); + endif + + flg = (a.w == b.w) && (a.x == b.x) && (a.y == b.y) && (a.z == a.z); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/exp.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,40 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{qexp} =} exp (@var{q}) +## Exponential of a quaternion. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function q = exp (q) + + if (nargin != 1) + print_usage (); + endif + + normv = normv (q); + exps = exp (q.w); + sinv = sin (normv); + + q.w = exps .* cos (normv); + q.x = exps .* (q.x ./ normv) .* sinv; + q.y = exps .* (q.y ./ normv) .* sinv; + q.z = exps .* (q.z ./ normv) .* sinv; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/horzcat.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,34 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Horizontal concatenation of quaternions. Used by Octave for "[q1, q2]". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = horzcat (varargin) + + tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! + + w = horzcat (tmp.w); + x = horzcat (tmp.x); + y = horzcat (tmp.y); + z = horzcat (tmp.z); + + q = quaternion (w, x, y, z); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/inv.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,42 @@ +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{qinv} =} inv (@var{q}) +## Return inverse of a quaternion. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.2 + +function a = inv (a) + + if (nargin != 1) + print_usage (); + endif + + if (isscalar (a.w)) + norm2 = norm2 (a); + a.w = a.w / norm2; + a.x = -a.x / norm2; + a.y = -a.y / norm2; + a.z = -a.z / norm2; + else + ## TODO: quaternion arrays + error ("quaternion: inv: implemented for scalar quaternions only"); + endif + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/ispure.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,33 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{flg} =} ispure (@var{q}) +## Return 1 if scalar part of quaternion is zero, otherwise return 0 +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function flg = ispure (a) + + if (nargin != 1) + print_usage (); + endif + + flg = all ((abs (a.w) < eps)(:)); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/ldivide.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,27 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Element-wise left division for quaternions. Used by Octave for "q1 .\\ q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = ldivide (a, b) + + q = a.^-1 .* b; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/log.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,61 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{qlog} =} log (@var{q}) +## Logarithmus naturalis of a quaternion. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function q = log (q) + + if (nargin != 1) + print_usage (); + endif + + normq = abs (q); + normv = normv (q); + acossq = acos (q.w ./ normq); + + q.w = log (normq); + q.x = (q.x ./ normv) .* acossq; + q.y = (q.y ./ normv) .* acossq; + q.z = (q.z ./ normv) .* acossq; + + ## FIXME: q = quaternion (2, 3, 4, 5) + ## p = log (exp (q)) + ## p.v is wrong, probably somehow related to acos + ## NOTE: p = exp (log (q)) is calculated correctly + ## NOTE: qtfm 1.9 returns the same "wrong" result + +endfunction + + +%!shared A, B +%! Aw = [2, 6, 10; 14, 18, 22]; +%! Ax = [3, 7, 11; 15, 19, 23]; +%! Ay = [4, 8, 12; 16, 20, 24]; +%! Az = [5, 9, 13; 17, 21, 25]; +%! A = quaternion (Aw, Ax, Ay, Az); +%! +%! B = exp (log (A)); +%! +%!assert (A.w, B.w, 1e-4); +%!assert (A.x, B.x, 1e-4); +%!assert (A.y, B.y, 1e-4); +%!assert (A.z, B.z, 1e-4);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/minus.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,38 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Subtraction of two quaternions. Used by Octave for "q1 - q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = minus (a, b) + + if (! isa (a, "quaternion")) + a = quaternion (a); + endif + + if (! isa (b, "quaternion")) + b = quaternion (b); + endif + + a.w = a.w - b.w; + a.x = a.x - b.x; + a.y = a.y - b.y; + a.z = a.z - b.z; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/mldivide.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,27 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Matrix left division for quaternions. Used by Octave for "q1 \\ q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = mldivide (a, b) + + q = inv (a) * b; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/mpower.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,56 @@ +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Matrix power operator of quaternions. Used by Octave for "q^x". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.2 + +function q = mpower (a, b) + + [r, c] = size (a); + + if (r != c) + error ("quaternion: mpower: quaternion matrix must be square"); + endif + + if (r == 1 && c == 1) # a scalar, b? + q = a .^ b; # b could be a quaternion + elseif (is_real_array (b) && isscalar (b) && fix (b) == b) + e = fix (abs (b)); + switch (sign (b)) + case -1 # q^-e + a = inv (a); + q = a; + case 0 # q^0 + q = eye (r); # alternative: q = quaternion (eye (r)) + return; + case 1; # q^e + q = a; + endswitch + for k = 2 : e + q *= a; # improvement?: q^8 = ((q^2)^2)^2, q^9 = (((q^2)^2)^2)*q + endfor + else + error ("quaternion: mpower: case not implemented yet"); + q = expm (logm (a) * b); # don't know whether this formula is correct + endif + + ## TODO: - q1 ^ q2 + ## - arrays + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/mrdivide.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,27 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Matrix right division for quaternions. Used by Octave for "q1 / q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = mrdivide (a, b) + + q = a * inv (b); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/mtimes.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,43 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Matrix multiplication of two quaternions. Used by Octave for "q1 * q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = mtimes (a, b) + + if (! isa (a, "quaternion")) + a = quaternion (a); + endif + + if (! isa (b, "quaternion")) + b = quaternion (b); + endif + + w = a.w*b.w - a.x*b.x - a.y*b.y - a.z*b.z; + x = a.y*b.z - a.z*b.y + a.w*b.x + a.x*b.w; + y = a.z*b.x - a.x*b.z + a.w*b.y + a.y*b.w; + z = a.x*b.y - a.y*b.x + a.w*b.z + a.z*b.w; + + a.w = w; + a.x = x; + a.y = y; + a.z = z; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/norm.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,38 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{n} =} norm (@var{q}) +## Norm of a quaternion. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function n = norm (a) + + if (nargin != 1) + print_usage (); + endif + + if (! isscalar (a.w)) + warning ("norm: use 'abs' to calculate the lengths of quaternion arrays"); + error ("norm: only the 2-norm of scalar quaternions is implemented until now"); + endif + + n = abs (a); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/plus.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,38 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Addition of two quaternions. Used by Octave for "q1 + q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = plus (a, b) + + if (! isa (a, "quaternion")) + a = quaternion (a); + endif + + if (! isa (b, "quaternion")) + b = quaternion (b); + endif + + a.w = a.w + b.w; + a.x = a.x + b.x; + a.y = a.y + b.y; + a.z = a.z + b.z; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/power.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,49 @@ +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch> +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Power operator of quaternions. Used by Octave for "q.^x". +## Exponent x can be scalar or of appropriate size. + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.3 + +function a = power (a, b) + + if (isa (b, "quaternion")) # exponent is a quaternion + a = exp (log (a) .* b); # a could be real, but log doesn't care + elseif (! isreal (b)) + error ("quaternion:invalidArgument", "quaternion: power: invalid exponent"); + elseif (b == -1) # special case for ldivide and rdivide + norm2 = norm2 (a); # a is quaternion because b is not, + a.w = a.w ./ norm2; # otherwise octave wouldn't call + a.x = -a.x ./ norm2; # quaternion's power operator. + a.y = -a.y ./ norm2; + a.z = -a.z ./ norm2; + else # exponent is real + na = abs (a); + nv = normv (a); + th = acos (a.w ./ na); + nab = na.^b; + snt = sin (b.*th); + a.w = nab .* cos (b.*th); + a.x = (a.x ./ nv) .* nab .* snt; + a.y = (a.y ./ nv) .* nab .* snt; + a.z = (a.z ./ nv) .* nab .* snt; + endif + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/private/norm2.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,29 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{norm2} =} norm2 (@var{q}) +## Return squared norm of a quaternion. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function ret = norm2 (a) + + ret = a.w.^2 + a.x.^2 + a.y.^2 + a.z.^2; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/private/normv.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,29 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{normv} =} normv (@var{q}) +## Return norm of the vector part. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function ret = normv (a) + + ret = sqrt (a.x.^2 + a.y.^2 + a.z.^2); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/quaternion.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,111 @@ +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{q} =} quaternion (@var{w}) +## @deftypefnx {Function File} {@var{q} =} quaternion (@var{x}, @var{y}, @var{z}) +## @deftypefnx {Function File} {@var{q} =} quaternion (@var{w}, @var{x}, @var{y}, @var{z}) +## Constructor for quaternions - create or convert to quaternion. +## +## @example +## q = w + x*i + y*j + z*k +## @end example +## +## Arguments @var{w}, @var{x}, @var{y} and @var{z} can be scalars or +## matrices, but they must be real and of equal size. If scalar part +## @var{w} or components @var{x}, @var{y} and @var{z} of the vector +## part are not specified, zero matrices of appropriate size are +## assumed. +## +## @strong{Example} +## @example +## @group +## octave:1> q = quaternion (2) +## q = 2 + 0i + 0j + 0k +## +## octave:2> q = quaternion (3, 4, 5) +## q = 0 + 3i + 4j + 5k +## +## octave:3> q = quaternion (2, 3, 4, 5) +## q = 2 + 3i + 4j + 5k +## @end group +## @end example +## @example +## @group +## octave:4> w = [2, 6, 10; 14, 18, 22]; +## octave:5> x = [3, 7, 11; 15, 19, 23]; +## octave:6> y = [4, 8, 12; 16, 20, 24]; +## octave:7> z = [5, 9, 13; 17, 21, 25]; +## octave:8> q = quaternion (w, x, y, z) +## q.w = +## 2 6 10 +## 14 18 22 +## +## q.x = +## 3 7 11 +## 15 19 23 +## +## q.y = +## 4 8 12 +## 16 20 24 +## +## q.z = +## 5 9 13 +## 17 21 25 +## +## octave:9> +## @end group +## @end example +## +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.2 + +function q = quaternion (a, b, c, d) + + switch (nargin) + case 1 + if (isa (a, "quaternion")) # quaternion (q) + q = a; + return; + elseif (is_real_array (a)) # quaternion (w) + b = c = d = zeros (size (a)); + else + print_usage (); + endif + case 3 # quaternion (x, y, z) + d = c; + c = b; + b = a; + a = zeros (size (a)); + case 4 # quaternion (w, x, y, z) + ## nothing to do here, just prevent case "otherwise" + otherwise + print_usage (); + endswitch + + if (! is_real_array (a, b, c, d)) + error ("quaternion: arguments must be real matrices"); + endif + + if (! size_equal (a, b, c, d)); + error ("quaternion: arguments must have identical sizes"); + endif + + q = class (struct ("w", a, "x", b, "y", c, "z", d), "quaternion"); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/rdivide.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,27 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Element-wise right division for quaternions. Used by Octave for "q1 ./ q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = rdivide (a, b) + + q = a .* b.^-1; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/rows.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,33 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{nr} =} rows (@var{q}) +## Return number of rows @var{nr} of quaternion array @var{q}. +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function r = rows (a) + + if (nargin != 1) + print_usage (); + endif + + r = rows (a.w); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/size.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,74 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{nvec} =} size (@var{q}) +## @deftypefnx {Function File} {@var{n} =} size (@var{q}, @var{dim}) +## @deftypefnx {Function File} {[@var{nx}, @var{ny}, @dots{}] =} size (@var{q}) +## Return size of quaternion arrays. +## +## @strong{Inputs} +## @table @var +## @item q +## Quaternion object. +## @item dim +## If given a second argument, @command{size} will return the size of the +## corresponding dimension. +## @end table +## +## @strong{Outputs} +## @table @var +## @item nvec +## Row vector. The first element is the number of rows and the second +## element the number of columns. If @var{q} is an n-dimensional array +## of quaternions, the n-th element of @var{nvec} corresponds to the +## size of the n-th dimension of @var{q}. +## @item n +## Scalar value. The size of the dimension @var{dim}. +## @item nx +## Number of rows. +## @item ny +## Number of columns. +## @item @dots{} +## Sizes of the 3rd to n-th dimensions. +## @end table +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.2 + +function varargout = size (a, b) + + switch (nargout) + case {0, 1} + switch (nargin) + case 1 # nvec = size (q) + varargout{1} = size (a.w); + case 2 # n = size (q, dim) + varargout{1} = size (a.w, b); + otherwise + print_usage (); + endswitch + + otherwise + if (nargin == 1) # [nx, ny, ...] = size (q) + varargout = num2cell (size (a.w)); + else + print_usage (); + endif + endswitch + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/subsasgn.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,64 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Subscripted assignment for quaternions. +## Used by Octave for "q.key = value". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.2 + +function q = subsasgn (q, idx, val) + + switch (idx(1).type) + case "()" # q(...) = val + if (length (idx(1).subs) == 1 && isa (val, "quaternion")) # required by horzcat, vertcat, cat, ... + q(idx(1).subs{:}) = val; # q = cellfun (@quaternion, varargin) + else # general case + val = quaternion (val); + w = subsasgn (q.w, idx, val.w); + x = subsasgn (q.x, idx, val.x); + y = subsasgn (q.y, idx, val.y); + z = subsasgn (q.z, idx, val.z); + q = quaternion (w, x, y, z); + endif + + case "." # q.w = val + if (! is_real_array (val)) + error ("quaternion: subsasgn: invalid argument type, require real array"); + endif + if (! size_equal (subsref (q.w, idx(2:end)), val)) + error ("quaternion: subsasgn: invalid argument size [%s], require dimensions [%s]", \ + num2str (size (val), "%d "), num2str (size (subsref (q.w, idx(2:end))), "%d ")); + endif + switch (tolower (idx(1).subs)) + case {"w", "s"} + q.w = subsasgn (q.w, idx(2:end), val); + case {"x", "i"} + q.x = subsasgn (q.x, idx(2:end), val); + case {"y", "j"} + q.y = subsasgn (q.y, idx(2:end), val); + case {"z", "k"} + q.z = subsasgn (q.z, idx(2:end), val); + otherwise + error ("quaternion: subsasgn: invalid subscript name '%s'", idx(1).subs); + endswitch + + otherwise + error ("quaternion: subsasgn: invalid subscript type '%s'", idx(1).type); + endswitch + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/subsref.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,60 @@ +## Copyright (C) 2010, 2011, 2012 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Subscripted reference for quaternions. Used by Octave for "q.w". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.4 + +function ret = subsref (q, s) + + if (numel (s) == 0) + ret = q; + return; + endif + + switch (s(1).type) + case "." # q.w + switch (tolower (s(1).subs)) + case {"w", "s"} # scalar part + ret = subsref (q.w, s(2:end)); + case {"x", "i"} + ret = subsref (q.x, s(2:end)); + case {"y", "j"} + ret = subsref (q.y, s(2:end)); + case {"z", "k"} + ret = subsref (q.z, s(2:end)); + case "v" # vector part, scalar part set to zero + q.w = zeros (size (q.w)); + ret = subsref (q, s(2:end)); + otherwise + error ("quaternion: invalid subscript name '%s'", s(1).subs); + endswitch + + case "()" # q(...) + w = subsref (q.w, s(1)); + x = subsref (q.x, s(1)); + y = subsref (q.y, s(1)); + z = subsref (q.z, s(1)); + tmp = quaternion (w, x, y, z); + ret = subsref (tmp, s(2:end)); + + otherwise + error ("quaternion: invalid subscript type '%s'", s(1).type); + endswitch + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/times.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,43 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Element-wise multiplication of two quaternions. Used by Octave for "q1 .* q2". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = times (a, b) + + if (! isa (a, "quaternion")) + a = quaternion (a); + endif + + if (! isa (b, "quaternion")) + b = quaternion (b); + endif + + w = a.w .* b.w - a.x .* b.x - a.y .* b.y - a.z .* b.z; + x = a.y .* b.z - a.z .* b.y + a.w .* b.x + a.x .* b.w; + y = a.z .* b.x - a.x .* b.z + a.w .* b.y + a.y .* b.w; + z = a.x .* b.y - a.y .* b.x + a.w .* b.z + a.z .* b.w; + + a.w = w; + a.x = x; + a.y = y; + a.z = z; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/transpose.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,34 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Transpose of a quaternion. Used by Octave for "q.'". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = transpose (a) + + if (nargin != 1) + print_usage (); + endif + + a.w = transpose (a.w); + a.x = transpose (a.x); + a.y = transpose (a.y); + a.z = transpose (a.z); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/uminus.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,30 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Unary minus of a quaternion. Used by Octave for "-q". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function a = uminus (a) + + a.w = -a.w; + a.x = -a.x; + a.y = -a.y; + a.z = -a.z; + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/unit.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,38 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{qn} =} unit (@var{q}) +## Normalize quaternion to length 1 (unit quaternion). +## +## @example +## q = w + x*i + y*j + z*k +## unit (q) = q ./ sqrt (w.^2 + x.^2 + y.^2 + z.^2) +## @end example +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function q = unit (a) + + if (nargin != 1) + print_usage (); + endif + + q = a ./ abs (a); + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/uplus.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,27 @@ +## Copyright (C) 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Unary plus of a quaternion. Used by Octave for "+q". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: November 2011 +## Version: 0.1 + +function a = uplus (a) + + ## nothing to do here + +endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/@quaternion/vertcat.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,34 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## Vertical concatenation of quaternions. Used by Octave for "[q1; q2]". + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = vertcat (varargin) + + tmp = cellfun (@quaternion, varargin); # uniformoutput = true ! + + w = vertcat (tmp.w); + x = vertcat (tmp.x); + y = vertcat (tmp.y); + z = vertcat (tmp.z); + + q = quaternion (w, x, y, z); + +endfunction
--- a/main/quaternion/inst/demoquat.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,259 +0,0 @@ -## Copyright (C) 1998, 1999, 2000, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this pogram; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} demoquat () -## Demonstrate the functions available for manipulating quaternions. -## -## Thanks to Mr. Charles Hall, Dr. Don Krupp and Dr. Larry Mullins at -## NASA's Marshall Space Flight Center for notes and instruction in -## use and conventions with quaternions. - A. S. Hodel -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function opt = demoquat () - - opt = 0; - quitopt = 5; - - while (opt != quitopt) - opt = menu ("Quaternion function demo (c) 1998 A. S. Hodel, a.s.hodel@eng.auburn.edu", - "quaternion construction/data extraction", - "simple quaternion functions", - "transformation functions", - "body-inertial frame demo", - "Quit"); - - switch(opt) - - case(1) - printf("Quaternion construction/data extraction\n"); - help quaternion - prompt - cmd = "q = quaternion(1,2,3,4)"; - run_cmd - disp("This format stores the i,j,k parts of the quaternion first;") - disp("the real part is stored last.") - prompt - disp(" ") - disp("i, j, and k are all square roots of -1; however they do not") - disp("commute under multiplication (discussed further with the function") - disp("qmult). Therefore quaternions do not commute under multiplcation:") - disp(" q1*q2 != q2*q1 (usually)") - prompt - - disp("Quaternions as rotations: unit quaternion to represent") - disp("rotation of 45 degrees about the vector [1 1 1]") - cmd = "degrees = pi/180; q1 = quaternion([1 1 1],45*degrees)"; - run_cmd - prompt - cmd = "real_q = cos(45*degrees/2)"; - run_cmd - printf("The real part of the quaternion q(4) is cos(theta/2).\n----\n\n"); - cmd = "imag_q = sin(45*degrees/2)*[1 1 1]/norm([1 1 1])" - run_cmd - disp("The imaginary part of the quaternion is sin(theta/2)*unit vector"); - disp("The constructed quaternion is a unit quaternion."); - prompt - disp("Can also extract both forms of the quaternion:") - disp("Vector/angle form of 1i + 2j + 3k + 4:") - cmd = "[vv,th] = quaternion(q)"; - run_cmd - cmd = "vv_norm = norm(vv)"; - run_cmd - disp("Returns the eigenaxis as a 3-d unit vector"); - disp("Check values: ") - cmd = "th_deg = th*180/pi"; - run_cmd - disp("") - disp("This concludes the quaternion construction/extraction demo."); - prompt - - case(2) - printf("Simple quaternion functions\n"); - cmd = "help qconj"; - run_cmd - cmd = "degrees = pi/180; q1 = quaternion([1 1 1],45*degrees)"; - run_cmd - cmd = "q2 = qconj(q1)"; - run_cmd - disp("The conjugate changes the sign of the complex part of the") - printf("quaternion.\n\n"); - prompt - printf("\n\n\nMultiplication of quaternions:\n"); - cmd = "help qmult"; - run_cmd - cmd = "help qinv" - run_cmd - disp("Inverse quaternion: q*qi = qi*q = 1:") - cmd = "q1i = qinv(q1)"; - run_cmd - cmd = "one = qmult(q1,q1i)"; - run_cmd - - printf("Conclusion of simple quaternion functions"); - prompt - - case(3) - printf("Transformation functions\n"); - disp("A problem with the discussion of coordinate transformations is that"); - disp("one must be clear on what is being transformed: does a rotation of"); - disp("theta degrees mean that you're rotating the VECTOR by theta degrees,"); - disp("also called the 'active convention,' or does it mean that you rotate "); - disp("the COORDINATE FRAME by theta degrees, also called the 'passive convention,' "); - disp("which is equivalent to rotating the VECTOR by (-theta) degrees. The"); - disp("functions in this demo use the active convention. I'll point out where"); - disp("this changes the code as the demo runs."); - disp(" -- The author"); - prompt - printf("\n\n"); - disp("Sequences of rotations:") - printf("\n\nRotation of a vector by 90 degrees about the reference z axis\n"); - cmd = "qz = quaternion([0 0 1], pi/2);"; - disp(cmd) ; eval(cmd); - printf("\n\nRotation of a vector by 90 degrees about the reference y axis\n"); - cmd="qy = quaternion([0 1 0], pi/2);"; - disp(cmd) ; eval(cmd); - printf("\n\nRotation of a vector by 90 degrees about the reference x axis\n"); - cmd="qx = quaternion([1 0 0], pi/2);"; - run_cmd - printf("\n\nSequence of three rotations: 90 degrees about x, then 90 degrees\n"); - disp("about y, then 90 degrees about z (all axes specified in the reference frame):"); - qchk = qmult(qz,qmult(qy,qx)); - cmd = "[vv,th] = quaternion(qchk), th_deg = th*180/pi"; - run_cmd - disp("The sequence of the three rotations above is equivalent to a single rotation") - disp("of 90 degrees about the y axis. Check:"); - cmd = "err = norm(qchk - qy)"; - run_cmd - - disp("Transformation of a quaternion by a quaternion:") - disp("The three quaternions above were rotations specified about") - disp("a single reference frame. It is often convenient to specify the"); - disp("eigenaxis of a rotation in a different frame (e.g., when computing"); - disp("the transformation rotation in terms of the Euler angles yaw-pitch-roll)."); - cmd = "help qtrans"; - run_cmd - disp("") - disp("NOTE: If the passive convention is used, then the above"); - disp("formula changes to v = qinv(q)*v*q instead of ") - disp("v = q*v*qinv(q).") - prompt - disp("") - disp("Example: Vectors in Frame 2 are obtained by rotating them from ") - disp(" from Frame 1 by 90 degrees about the x axis (quaternion qx)") - disp(" A quaternion in Frame 2 rotates a vector by 90 degrees about") - disp(" the Frame 2 y axis (quaternion qy). The equivalent rotation") - disp(" in the reference frame is:") - cmd = "q_eq = qtrans(qy,qx); [vv,th] = quaternion(q_eq)"; - run_cmd - disp("The rotation is equivalent to rotating about the reference z axis") - disp("by 90 degrees (quaternion qz)") - prompt - - disp("Transformation of a vector by a quaternion"); - cmd = "help qtransv"; - run_cmd - - disp("NOTE: the above formula changes if the passive quaternion ") - disp("is used; the cross product term is subtracted instead of added."); - prompt - disp("Example: rotate the vector [1,1,1] by 90 degrees about the y axis"); - cmd = "vec_r = qtransv([1,1,1],qy)"; - run_cmd - prompt - disp("Equivalently, one may multiply by qtransvmat:") - cmd = "help qtransvmat"; - run_cmd - disp("NOTE: the passive quaternion convention would use the transpose") - disp("(inverse) of the orthogonal matrix returned by qtransvmat."); - prompt - cmd = "vec_r_2 = qtransvmat(qy)*[1;1;1]; vec_err = norm(vec_r - vec_r_2)"; - run_cmd - - disp("") - disp("The last transformation function is the derivative of a quaternion") - disp("Given rotation rates about the reference x, y, and z axes."); - cmd = "help qderivmat"; - run_cmd - disp("") - disp("Example:") - disp("Frame is rotating about the z axis at 1 rad/s") - cmd = "Omega = [0,0,1]; Dmat = qderivmat(Omega)"; - run_cmd - disp("Notice that Dmat is skew symmetric, as it should be.") - disp("expm(Dmat*t) is orthogonal, so that unit quaternions remain") - disp("unit quaternions as the rotating frame precesses."); - disp(" ") - disp("This concludes the transformation demo."); - prompt; - - case(4) - printf("Body-inertial frame demo: Look at the source code for\n"); - printf("demoquat.m and qcoordinate_plot.m to see how it's done.\n"); - - # i,j,k units - iv = quaternion(1,0,0,0); jv = quaternion(0,1,0,0); - kv = quaternion(0,0,1,0); - - # construct quaternion to desired view. - degrees = pi/180; daz = 45*degrees; del = -30*degrees; - qazimuth = quaternion([0,0,1],daz); - qelevation = quaternion([cos(daz),sin(daz),0],del); - qview = qmult(qelevation,qazimuth); - - # inertial frame i, j, k axes. - iif = iv; jf = qtrans(jv,iv); kf = qtrans(kv,iv); - - # rotation steps - th = 0:5:20; ov = ones(size(th)); myth = [th,max(th)*ov ; 0*ov,th]; - - # construct yaw-pitch-roll cartoon - for kk=1:length(myth(1,:)) - thy = myth(1,kk); - thp = myth(2,kk); - - qyaw = quaternion([0,0,1],thy*pi/180); - [jvy,th] = quaternion(qtrans(jf,qyaw)); - qpitch = quaternion(jvy(1:3),thp*pi/180); - qb = qmult(qpitch, qyaw); - qi = quaternion([1, 0, 0],180*degrees); - - printf("yaw=%8.4f, pitch=%8.4f, \n qbi = (%8.4f)i + (%8.4e)j + (%8.4f)k + (%8.4f)\n",thy,thp, ... - qb(1), qb(2), qb(3), qb(4)); - [vv,th] = quaternion(qb); - printf(" = (vector) = [%8.4f %8.4f %8.4f], th=%5.2f deg\n", ... - vv(1), vv(2), vv(3), th*180/pi); - fflush (stdout); - qb = qmult(qb,qi); - title(sprintf("yaw=%5.2f deg, pitch=%5.2f deg",thy,thp)) - qcoordinate_plot(qi,qb,qview); - drawnow (); - endfor - - case(quitopt) - printf ("Exiting quaternion demo\n"); - - otherwise - error ("invalid option %f", opt); - - endswitch - endwhile - -endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/q2rot.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,93 @@ +## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 Auburn University +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {[@var{axis}, @var{angle}] =} q2rot (@var{q}) +## Extract vector/angle form of a unit quaternion @var{q}. +## +## @strong{Inputs} +## @table @var +## @item q +## Unit quaternion describing the rotation. +## @end table +## +## @strong{Outputs} +## @table @var +## @item axis +## Eigenaxis as a 3-d unit vector @code{[x, y, z]}. +## @item angle +## Rotation angle in radians. The positive direction is +## determined by the right-hand rule applied to @var{axis}. +## @end table +## +## @strong{Example} +## @example +## @group +## octave:1> axis = [0, 0, 1] +## axis = +## 0 0 1 +## octave:2> angle = pi/4 +## angle = 0.78540 +## octave:3> q = rot2q (axis, angle) +## q = 0.9239 + 0i + 0j + 0.3827k +## octave:4> [vv, th] = q2rot (q) +## vv = +## 0 0 1 +## th = 0.78540 +## octave:5> theta = th*180/pi +## theta = 45.000 +## octave:6> +## @end group +## @end example +## +## @end deftypefn + +## Adapted from: quaternion by A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function [vv, theta] = q2rot (q) + + if (nargin != 1 || nargout != 2) + print_usage (); + endif + + if (! isa (q, "quaternion") || ! isscalar (q.w)) + error ("q2rot: require scalar quaternion as input"); + endif + + if (abs (norm (q) - 1) > 1e-12) + warning ("q2rot: ||q||=%e, setting=1 for vv, theta", norm (q)); + q = unit (q); + endif + + s = q.s; + vv = [q.x, q.y, q.z]; + + theta = acos (s) * 2; + + if (abs (theta) > pi) + theta = theta - sign (theta) * pi; + endif + + sin_th_2 = norm (vv); + + if (sin_th_2 != 0) + vv ./= sin_th_2; + endif + +endfunction \ No newline at end of file
--- a/main/quaternion/inst/qconj.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,42 +0,0 @@ -## Copyright (C) 1998, 2000, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qconj (@var{q}) -## Conjugate of a quaternion. -## -## @example -## q = [w, x, y, z] = w*i + x*j + y*k + z -## qconj (q) = -w*i -x*j -y*k + z -## @end example -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function retval = qconj (q) - - if (nargin != 1 ) - print_usage (); - endif - - [a, b, c, d] = quaternion (q); - - retval = quaternion (-a, -b, -c, d); - -endfunction -
--- a/main/quaternion/inst/qcoordinate_plot.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,131 +0,0 @@ -## Copyright (C) 1998, 1999, 2000, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qcoordinate_plot (@var{qf}, @var{qb}, @var{qv}) -## Plot in the current figure a set of coordinate axes as viewed from -## the orientation specified by quaternion @var{qv}. Inertial axes are -## also plotted: -## -## @table @var -## @item qf -## Quaternion from reference (x,y,z) to inertial. -## @item qb -## Quaternion from reference to body. -## @item qv -## Quaternion from reference to view angle. -## @end table -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function qcoordinate_plot (qf, qb, qv) - - if (nargin != 3 ) - print_usage (); - endif - - degrees = pi / 180; - d180 = 180 * degrees; - - ## construct coordinate transformation to view frame - - cm = qtransvmat(qv); - - p1 = [-1, -1, 1]; - p2 = [-1, -1, -1]; - p3 = [ 1, -1, -1]; - p4 = [ 1, -1, 1]; - p5 = [-1, 1, 1]; - p6 = [ 1, 1, 1]; - p7 = [ 1, 1, -1]; - p8 = [-1, 1, -1]; - - ## outline positive quadrant - - box1 = cm * [p4; p6; p5; p6; p7]'; - - ## outline rest of the box - - box2 = cm * [p7; p8; p5; p1; p4; p3; p7; p3; p2; p1; p2; p8]'; - - ## compute inertial to body rotation eigenaxis - ## qb = qbf*qf => qbf = qb/qf - ## - ## need to use inverse quaternion to rotate axes - - qbf = qinv (qmult (qb, qinv (qf))); - - [eaxv, th_eig] = quaternion (qbf); - - ## draw 1/3 circle in x-y plane around a unit z axis - - th = (0:-12:-120) * degrees * sign (th_eig); - lth = length (th); - - cpts = [0, 0, 0.1*cos(th); - 0, 0, 0.1*sin(th); - 0, 1, 1*ones(1,lth)]; - - ## rotate the 1/3 circle around eigenaxis of inertial to body rotation - ## qez = qe/qz = rotation to get from z axis to eigenaxis. - ## This rotates the 1/3 circle from x-y plane to the plane normal to - ## eigenaxis - - qez = qmult (qbf, qinv (quaternion (0, 0, 1, 0))); - eig_xm = qtransvmat (qez); - cpts = cm*eig_xm * cpts; - - ## transform inertial and body quaternions to view coordinates (rotate - ## by azimuth, elevation) - - qfm = qtransvmat (qf); - qbm = qtransvmat (qf); - - qf = qmult (qv, qf); - qb = qmult (qv, qb); - - ## get coordinate axes in inertial and reference frame - - jnk = qtransvmat (qf); - ifv = jnk(:,1); - jfv = jnk(:,2); - kfv = jnk(:,3); - - jnk = qtransvmat (qb); - ibv = jnk(:,1); - jbv = jnk(:,2); - kbv = jnk(:,3); - - axis ([-2, 2, -2, 2], "square"); - - [vv, theta] = quaternion (qb); - - xlabel (sprintf ("rotate about eigenaxis %5.2f deg", th_eig/degrees)); - - plot ([ibv(1), 0], [ibv(3), 0], "-@11;x (body);", - [0, jbv(1)], [0, jbv(3)], "-@21;y (body);", - [0, kbv(1)], [0, kbv(3)], "-@32;z (body);", - [ifv(1), 0], [ifv(3), 0], "-@13;x (inertial);", - [0, jfv(1)], [0, jfv(3)], "-@23;y (inertial);", - [0, kfv(1)], [0, kfv(3)], "-@34;z (inertial);", - cpts(1,:), cpts(3,:), ".-6 ;eigenaxis;", - box2(1,:), box2(3,:), "-4;;", - box1(1,:), box1(3,:), "-5;;"); - -endfunction
--- a/main/quaternion/inst/qderiv.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,58 +0,0 @@ -## Copyright (C) 1998, 2000, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qderiv (omega) -## Derivative of a quaternion. -## -## Let Q be a quaternion to transform a vector from a fixed frame to -## a rotating frame. If the rotating frame is rotating about the -## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative -## of Q is given by -## -## @example -## Q' = qderivmat (omega) * Q -## @end example -## -## If the passive convention is used (rotate the frame, not the vector), -## then -## -## @example -## Q' = -qderivmat (omega) * Q -## @end example -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function Dmat = qderivmat (Omega) - - if (nargin != 1) - print_usage (); - endif - - Omega = vec (Omega); - - if (length (Omega) != 3) - error ("qderivmat: Omega must be a length 3 vector"); - endif - - Dmat = 0.5 * [ 0.0, Omega(3), -Omega(2), Omega(1); - -Omega(3), 0.0, Omega(1), Omega(2); - Omega(2), -Omega(1), 0.0, Omega(3); - -Omega(1), -Omega(2), -Omega(3), 0.0 ]; -endfunction
--- a/main/quaternion/inst/qderivmat.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,58 +0,0 @@ -## Copyright (C) 1998, 2000, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qderivmat (@var{omega}) -## Derivative of a quaternion. -## -## Let Q be a quaternion to transform a vector from a fixed frame to -## a rotating frame. If the rotating frame is rotating about the -## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative -## of Q is given by -## -## @example -## Q' = qderivmat (omega) * Q -## @end example -## -## If the passive convention is used (rotate the frame, not the vector), -## then -## -## @example -## Q' = -qderivmat (omega) * Q. -## @end example -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function Dmat = qderivmat (Omega) - - if (nargin != 1 ) - print_usage (); - endif - - Omega = vec (Omega); - - if (length (Omega) != 3) - error ("qderivmat: Omega must be a length 3 vector"); - endif - - Dmat = 0.5 * [ 0.0, Omega(3), -Omega(2), Omega(1); - -Omega(3), 0.0, Omega(1), Omega(2); - Omega(2), -Omega(1), 0.0, Omega(3); - -Omega(1), -Omega(2), -Omega(3), 0.0 ]; -endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/qi.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,48 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## @deftypefn {Function File} {} qi +## Create x-component of a quaternion's vector part. +## +## @example +## q = w + x*qi + y*qj + z*qk +## @end example +## +## @strong{Example} +## @example +## @group +## octave:1> q1 = quaternion (1, 2, 3, 4) +## q1 = 1 + 2i + 3j + 4k +## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk +## q2 = 1 + 2i + 3j + 4k +## octave:3> +## @end group +## @end example +## +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = qi + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (0, 1, 0, 0); + +endfunction \ No newline at end of file
--- a/main/quaternion/inst/qinv.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,43 +0,0 @@ -## Copyright (C) 1998, 2000, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qinv (@var{q}) -## Return the inverse of a quaternion. -## -## @example -## q = [w, x, y, z] = w*i + x*j + y*k + z -## qmult (q, qinv (q)) = 1 = [0 0 0 1] -## @end example -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function retval = qinv (q) - - if (nargin != 1) - print_usage (); - endif - - if (norm (q) != 0) - retval = qconj (q) / sum (q .* q); - else - error ("qinv: zero quaternion passed!"); - endif - -endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/qj.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,48 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## @deftypefn {Function File} {} qj +## Create y-component of a quaternion's vector part. +## +## @example +## q = w + x*qi + y*qj + z*qk +## @end example +## +## @strong{Example} +## @example +## @group +## octave:1> q1 = quaternion (1, 2, 3, 4) +## q1 = 1 + 2i + 3j + 4k +## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk +## q2 = 1 + 2i + 3j + 4k +## octave:3> +## @end group +## @end example +## +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = qj + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (0, 0, 1, 0); + +endfunction \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/qk.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,48 @@ +## Copyright (C) 2010 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## @deftypefn {Function File} {} qk +## Create z-component of a quaternion's vector part. +## +## @example +## q = w + x*qi + y*qj + z*qk +## @end example +## +## @strong{Example} +## @example +## @group +## octave:1> q1 = quaternion (1, 2, 3, 4) +## q1 = 1 + 2i + 3j + 4k +## octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk +## q2 = 1 + 2i + 3j + 4k +## octave:3> +## @end group +## @end example +## +## @end deftypefn + +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = qk + + if (nargin != 0) + print_usage (); + endif + + q = quaternion (0, 0, 0, 1); + +endfunction \ No newline at end of file
--- a/main/quaternion/inst/qmult.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,57 +0,0 @@ -## Copyright (C) 1998, 2000, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qmult (@var{a}, @var{b}) -## Multiply two quaternions. -## -## @example -## [w, x, y, z] = w*i + x*j + y*k + z -## @end example -## -## @noindent -## identities: -## -## @example -## i^2 = j^2 = k^2 = -1 -## ij = k jk = i -## ki = j kj = -i -## ji = -k ik = -j -## @end example -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function retval = qmult (a, b) - - if (nargin != 2 ) - print_usage (); - endif - - [a1, b1, c1, d1] = quaternion (a); - [a2, b2, c2, d2] = quaternion (b); - - ri = b1*c2 - c1*b2 + d1*a2 + a1*d2; - rj = c1*a2 - a1*c2 + d1*b2 + b1*d2; - rk = a1*b2 - b1*a2 + d1*c2 + c1*d2; - rr = -(a1*a2 + b1*b2 + c1*c2) + d1*d2; - - retval = quaternion (ri, rj, rk, rr); - -endfunction -
--- a/main/quaternion/inst/qtrans.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,41 +0,0 @@ -## Copyright (C) 1998, 2000, 2002, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qtrans (@var{v}, @var{q}) -## Transform the unit quaternion @var{v} by the unit quaternion @var{q}. -## Returns @code{@var{v} = @var{q}*@var{v}/@var{q}}. -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function v = qtrans (v, q) - - if (nargin != 2) - print_usage (); - endif - - if (! isvector (v) || length (v) != 4) - error ("qtrans: v(%d,%d) must be a quaternion", rows (v), columns (v)); - elseif (! isvector (q) || length (q) != 4) - error ("qtrans: q(%d,%d) must be a quaternion", rows (q), columns (q)); - endif - - v = qmult (q, qmult (v, qinv (q))); - -endfunction
--- a/main/quaternion/inst/qtransv.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,50 +0,0 @@ -## Copyright (C) 1998, 2000, 2002, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qtransv (@var{v}, @var{q}) -## Transform the 3-D vector @var{v} by the unit quaternion @var{q}. -## Return a column vector. -## -## @example -## vi = (2*real(q)^2 - 1)*vb + 2*imag(q)*(imag(q)'*vb) -## + 2*real(q)*cross(imag(q),vb) -## @end example -## -## @noindent -## Where imag(q) is a column vector of length 3. -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function vi = qtransv (vb, qib) - - if (! isvector (vb) || length (vb) != 3) - error ("qtransv: v(%d,%d) must be a 3-D vector", rows (vb), columns (vb)); - elseif (! isvector (qib) || length (qib) != 4) - error ("qtransv: q(%d,%d) must be a quaternion", rows (qib), columns (qib)); - elseif (max (abs (imag (vb))) + max (abs (imag (qib))) != 0) - error ("qtransv: input values must be real"); - endif - - qr = qib(4); - qimag = vec (qib(1:3)); - vb = vec (vb); - vi = (2*qr^2 - 1)*vb + 2*qimag*(qimag'*vb) + 2*qr*cross (qimag, vb); - -endfunction
--- a/main/quaternion/inst/qtransvmat.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,52 +0,0 @@ -## Copyright (C) 1998, 2000, 2002, 2004, 2005, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {} qtransvmat (@var{qib}) -## Construct a 3x3 transformation matrix from quaternion @var{qib} that -## is equivalent to rotation of th radians about axis @var{vv}, where -## @code{[@var{vv}, @var{th}] = quaternion (@var{qib})}. -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function Aib = qtransvmat (qib) - - if (nargin != 1) - print_usage (); - endif - - if (! isvector(qib) || length (qib) != 4) - error ("qtransvmat: q(%d,%d) must be a quaternion", rows (qib), \ - columns (qib)); - elseif (max (abs (imag (qib))) != 0) - error ("qtransvmat: input values must be real"); - endif - - - Aib = [(2.*(qib(1)^2 + qib(4)^2) -1.), ... - (2.*(qib(1)*qib(2)-qib(3)*qib(4))), ... - (2.*(qib(1)*qib(3)+qib(2)*qib(4))); - (2.*(qib(1)*qib(2)+qib(3)*qib(4))), ... - (2.*(qib(2)*qib(2)+qib(4)*qib(4))-1.), ... - (2.*(qib(2)*qib(3)-qib(1)*qib(4))); - (2.*(qib(1)*qib(3)-qib(2)*qib(4))), ... - (2.*(qib(2)*qib(3)+qib(1)*qib(4))), ... - (2.*(qib(3)*qib(3)+qib(4)*qib(4))-1.)]; - -endfunction
--- a/main/quaternion/inst/quaternion.m Wed Mar 28 02:57:39 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,114 +0,0 @@ -## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 -## Auburn University. All rights reserved. -## -## This program is free software; you can redistribute it and/or modify it -## under the terms of the GNU General Public License as published by -## the Free Software Foundation; either version 3 of the License, or (at -## your option) any later version. -## -## This program is distributed in the hope that it will be useful, but -## WITHOUT ANY WARRANTY; without even the implied warranty of -## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -## General Public License for more details. -## -## You should have received a copy of the GNU General Public License -## along with this program; see the file COPYING. If not, see -## <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}] =} quaternion (w) -## @deftypefnx {Function File} {[@var{vv}, @var{theta}] =} quaternion (w) -## @deftypefnx {Function File} {@var{w} =} quaternion (@var{a}, @var{b}, @var{c}, @var{d}) -## @deftypefnx {Function File} {@var{w} =} quaternion (@var{vv}, @var{theta}) -## Construct or extract a quaternion -## -## @example -## w = a*i + b*j + c*k + d -## @end example -## -## @noindent -## from given data. -## @end deftypefn - -## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> -## Adapted-By: jwe - -function [a, b, c, d] = quaternion (w, x, y, z) - - switch (nargin) - case(1) - if (! (isvector (w) && length (w) == 4)) - error ("input vector must be of length 4)"); - endif - ## extract data - switch (nargout) - case(4) - a = w(1); - b = w(2); - c = w(3); - d = w(4); - - case(2) - if (abs (norm (w) - 1) > 1e-12) - warning ("quaternion: ||w||=%e, setting=1 for vv, theta", norm(w)); - w = w/norm(w); - endif - [a, b, c, d] = quaternion (w); - theta = acos (d) * 2; - if (abs (theta) > pi) - theta = theta - sign (theta) * pi; - endif - sin_th_2 = norm ([a, b, c]); - - if (sin_th_2 != 0) - vv = [a, b, c] / sin_th_2; - else - vv = [a, b, c]; - endif - a = vv; - b = theta; - otherwise - print_usage (); - endswitch - - case(2) - if (nargout > 1) - print_usage (); - endif - vv = w; - theta = x; - - if (! isvector (vv) || length (vv) != 3) - error ("vv must be a length three vector"); - elseif (! isscalar (theta)) - error ("theta must be a scalar"); - elseif (norm (vv) == 0) - error ("quaternion: vv is zero"); - elseif (abs (norm (vv) - 1) > 1e-12) - warning ("quaternion: ||vv|| != 1, normalizing") - vv = vv / norm (vv); - endif - - if (abs (theta) > 2*pi) - warning ("quaternion: |theta| > 2 pi, normalizing") - theta = rem (theta, 2*pi); - endif - vv = vv * sin (theta / 2); - d = cos (theta / 2); - a = quaternion (vv(1), vv(2), vv(3), d); - - case(4) - if (nargout > 1) - print_usage (); - endif - if (! (isscalar (w) && isscalar (x) && isscalar (y) && isscalar (z))) - error ("input values must be scalars"); - endif - a = [w, x, y, z]; - - otherwise - print_usage (); - - endswitch - -endfunction
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/rot2q.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,95 @@ +## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 Auburn University +## Copyright (C) 2010, 2011 Lukas F. Reichlin +## +## This program is free software: you can redistribute it and/or modify +## it under the terms of the GNU General Public License as published by +## the Free Software Foundation, either version 3 of the License, or +## (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program. If not, see <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{q} =} rot2q (@var{axis}, @var{angle}) +## Create unit quaternion @var{q} which describes a rotation of +## @var{angle} radians about the vector @var{axis}. This function uses +## the active convention where the vector @var{axis} is rotated by @var{angle} +## radians. If the coordinate frame should be rotated by @var{angle} +## radians, also called the passive convention, this is equivalent +## to rotating the @var{axis} by @var{-angle} radians. +## +## @strong{Inputs} +## @table @var +## @item axis +## Vector @code{[x, y, z]} describing the axis of rotation. +## @item angle +## Rotation angle in radians. The positive direction is +## determined by the right-hand rule applied to @var{axis}. +## @end table +## +## @strong{Outputs} +## @table @var +## @item q +## Unit quaternion describing the rotation. +## @end table +## +## @strong{Example} +## @example +## @group +## octave:1> axis = [0, 0, 1]; +## octave:2> angle = pi/4; +## octave:3> q = rot2q (axis, angle) +## q = 0.9239 + 0i + 0j + 0.3827k +## octave:4> v = quaternion (1, 1, 0) +## v = 0 + 1i + 1j + 0k +## octave:5> vr = q * v * conj (q) +## vr = 0 + 0i + 1.414j + 0k +## octave:6> +## @end group +## @end example +## +## @end deftypefn + +## Adapted from: quaternion by A. S. Hodel <a.s.hodel@eng.auburn.edu> +## Author: Lukas Reichlin <lukas.reichlin@gmail.com> +## Created: May 2010 +## Version: 0.1 + +function q = rot2q (vv, theta) + + if (nargin != 2 || nargout != 1) + print_usage (); + endif + + if (! isvector (vv) || length (vv) != 3) + error ("vv must be a length three vector"); + endif + + if (! isscalar (theta)) + error ("theta must be a scalar"); + endif + + if (norm (vv) == 0) + error ("quaternion: vv is zero"); + endif + + if (abs (norm (vv) - 1) > 1e-12) + warning ("quaternion: ||vv|| != 1, normalizing") + vv = vv / norm (vv); + endif + + if (abs (theta) > 2*pi) + warning ("quaternion: |theta| > 2 pi, normalizing") + theta = rem (theta, 2*pi); + endif + + vv = vv * sin (theta / 2); + d = cos (theta / 2); + q = quaternion (d, vv(1), vv(2), vv(3)); + +endfunction \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/inst/test_quaternion.m Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,4 @@ +test @quaternion/blkdiag +test @quaternion/diag +test @quaternion/diff +test @quaternion/log \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/src/Makefile Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,8 @@ +all: is_real_array.oct + +# helper +is_real_array.oct: is_real_array.cc + mkoctfile is_real_array.cc + +clean: + rm *.o core octave-core *.oct *~
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/quaternion/src/is_real_array.cc Wed Mar 28 03:16:58 2012 +0000 @@ -0,0 +1,60 @@ +/* + +Copyright (C) 2011 Lukas F. Reichlin + +This file is part of LTI Syncope. + +LTI Syncope is free software: you can redistribute it and/or modify +it under the terms of the GNU General Public License as published by +the Free Software Foundation, either version 3 of the License, or +(at your option) any later version. + +LTI Syncope is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU General Public License for more details. + +You should have received a copy of the GNU General Public License +along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>. + +Return true if argument is a real array. + +Author: Lukas Reichlin <lukas.reichlin@gmail.com> +Created: November 2011 +Version: 0.2 + +*/ + +#include <octave/oct.h> + +DEFUN_DLD (is_real_array, args, nargout, + "-*- texinfo -*-\n\ +@deftypefn {Loadable Function} {} is_real_array (@var{a}, @dots{})\n\ +Return true if argument is a real array.\n\ +@var{[]} is a valid array.\n\ +Avoid nasty stuff like @code{true = isreal (\"a\")}.\n\ +@end deftypefn") +{ + octave_value retval = true; + int nargin = args.length (); + + if (nargin == 0) + { + print_usage (); + } + else + { + for (int i = 0; i < nargin; i++) + { + // args(i).ndims () should be always >= 2 + if (args(i).ndims () < 2 || ! args(i).is_numeric_type () + || ! args(i).is_real_type ()) + { + retval = false; + break; + } + } + } + + return retval; +}