{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "rolling.mws make arrows \+ myself" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 "xstart, ystart, xlength, ylength , thickness, color specified" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "head part s are 0.15 of length, at Pi/8 = 22.5 degrees" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "With basic arrow done, one want s to do a loop and put in various arrows" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "One wants to add arrows vectoriall y too. Just add components." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 "Rolling wheel, vcm arrow green, vtan arrow red, total v over ground is black" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "mo:=0.15;cs:=cos(Pi/8);sn:=sin(Pi/8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#moG$\"#:!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c sG,$*$,&\"\"#\"\"\"*$F(#F)F(F)F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#snG,$*$,&\"\"#\"\"\"*$F(#F)F(!\"\"F+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 34 "arrwbody:=[[xo,yo],[xo+lx,yo+ly]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)arrwbodyG7$7$%#xoG%#yoG7$,&F'\"\"\"%#lxGF+,&F(F +%#lyGF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "arrwhd1:=[[xo+l x,yo+ly],[xo+lx-mo*lx*cs-mo*ly*sn,yo+ly-mo*ly*cs+mo*lx*sn]];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(arrwhd1G7$7$,&%#xoG\"\"\"%#lxGF),&%#yoGF) %#lyGF)7$,*F(F)F*F)*&F*F),&\"\"#F)*$F2#F)F2F)F4$!+++++v!#6*&F-F),&F2F) F3!\"\"F4F5,*F,F)F-F)*&F-F)F1F4F5*&F*F)F9F4$\"+++++vF7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "arrwhd2:=[[xo+lx,yo+ly],[xo+lx-mo*l x*cs+mo*ly*sn,yo+ly-mo*ly*cs-mo*lx*sn]];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(arrwhd2G7$7$,&%#xoG\"\"\"%#lxGF),&%#yoGF)%#lyGF)7$,*F(F)F*F)* &F*F),&\"\"#F)*$F2#F)F2F)F4$!+++++v!#6*&F-F),&F2F)F3!\"\"F4$\"+++++vF7 ,*F,F)F-F)*&F-F)F1F4F5*&F*F)F9F4F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "arrw:=\{arrwbody,arrwhd1,arrwhd2\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%arrwG<%7$7$,&%#xoG\"\"\"%#lxGF*,&%#yoGF*%#lyGF*7$ ,*F)F*F+F**&F+F*,&\"\"#F**$F3#F*F3F*F5$!+++++v!#6*&F.F*,&F3F*F4!\"\"F5 F6,*F-F*F.F**&F.F*F2F5F6*&F+F*F:F5$\"+++++vF87$F'7$,*F)F*F+F*F1F6F9F?, *F-F*F.F*F=F6F>F67$7$F)F-F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "plot(subs(xo=0,yo=0,lx=-3,ly=-2,arrw),thickness=3,color=black);" } }{PARA 13 "" 1 "" {INLPLOT "6'-%'CURVESG6#7$7$$!\"$\"\"!$!\"#F*7$$!1[% z+Cf!*p#!#:$!1CBo&fG1b\"F0-F$6#7$F'7$$!1%Rg1=\\%pCF0$!1/4\"[oV]*=F0-F$ 6#7$7$F*F*F'-%*THICKNESSG6#\"\"$-%'COLOURG6&%$RGBGF*F*F*" 2 322 322 322 2 0 1 3 2 6 0 4 1 1.000000 45.000000 45.000000 10030 10061 10056 10073 0 0 0 20030 0 12010 0 0 0 0 0 0 0 1 1 0 0 0 165 235 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "arrwsum:=subs(xo=0,yo=0,l x=1+3,ly=2+6,arrw);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(arrwsumG<%7$ 7$\"\"%\"\")7$,(F(\"\"\"*$,&\"\"#F,*$F/#F,F/F,F1$!+++++I!#5*$,&F/F,F0! \"\"F1$\"+++++gF4,(F)F,F-$!+++++gF4F5F27$F'7$,(F(F,F-F2F5F;,(F)F,F-F;F 5$\"+++++IF47$7$\"\"!FEF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot(arrwsum,color=black,thickness=3,scaling=constrained);" }} {PARA 13 "" 1 "" {INLPLOT "6(-%'CURVESG6#7$7$$\"\"%\"\"!$\"\")F*7$$\"1 N8L*R#*[!R!#:$\"1-uc,XthmF0-F$6#7$F'7$$\"1?^lh@X')HF0$\"14bS?Y&47(F0-F $6#7$7$F*F*F'-%*THICKNESSG6#\"\"$-%'COLOURG6&%$RGBGF*F*F*-%(SCALINGG6# %,CONSTRAINEDG" 2 322 322 322 2 0 1 3 2 6 0 4 1 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 183 -8668 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "vcm:=Pi;radius:=4; \+ omega:=-vcm/radius; # rolling w/o slipping" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$vcmG%#PiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'radi usG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&omegaG,$%#PiG#!\"\"\"\" %" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "npts:=7; m1:=1/4;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%nptsG\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#m1G#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "for i from 0 to npts do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "x:=radius*cos(omega*i);y:=radius+radius*sin(omega*i); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "acm.i:=plot(subs(xo=x,yo=y,lx=m 1*vcm,ly=0,arrw),color=green,thickness=2,scaling=constrained);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "atn.i:=plot(subs(xo=x,yo=y,lx=m1*v cm*sin(omega*i),ly=-m1*vcm*cos(omega*i),arrw),thickness=2,color=red,sc aling=constrained);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 132 "add.i:=plot(subs(xo=x,yo=y,lx=m1*vcm+m1*vcm *sin(omega*i),ly=-m1*vcm*cos(omega*i),arrw),thickness=4,color=black,sc aling=constrained);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "tot.i:=displ ay(\{acm.i,atn.i,add.i\});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "display(\{acm.(0..npts),at n.(0..npts),add.(0..npts)\});" }}{PARA 13 "" 1 "" {INLPLOT "6co-%'CURV ESG6%7$7$$\"\"%\"\"!$\"1_DgO=g9K!#:7$$\"1E8uHQ3XSF-$\"1!y2)HQWBLF--%'C OLOURG6&%$RGBG$\"*++++\"!\")F*F*-%*THICKNESSG6#\"\"#-F$6%7$F'7$$\"1u'e -<;\\&RF-F1F3F:-F$6%7$7$F(F(F'F3F:-F$6%7$7$$\"1RO9)GDQh$F-$\"15QDvGdr6 F-7$$\"15%Q\\H$)\\]$F-$\"1%[7b/*[E6F--F46&F6F*F7F*F:-F$6%7$7$$\"1!>YZ7 F%GGF-FNFKFUF:-F$6%7$FK7$FQ$\"1O^*\\qcm@\"F-FUF:-F$6%7$7$$\"1')f,#\\(y $Q$F-$\"1&RwuvmIF'F-7$$\"1gYFiOqQLF-$\"1B;o](3>Q'F-F3F:-F$6%7$F`o7$$\" 1d2\"))\\X\\F$F-$\"1@x@(e]\"=jF-F3F:-F$6%7$7$Fen$\"1!>YZ7F%GoF-F`oF3F: -F$6%7$7$$\"1[uRj\")R&y%F-F(7$$\"1?A>qhbwYF-F/FUF:-F$6%7$F[q7$F_qFBFUF :-F$6%7$FGF[qFUF:-F$6%7$FZ7$$\"1&RwuvmIF#F-$\"1R,%)z]7ih!#;F3F:-F$6%7$ F[r7$$\"1B;o](3>Q#F-$\"1*R`sPjHh'F`rF3F:-F$6%7$F[r7$$\"1?x@(e]\"=BF-$ \"1DC*=,X0D(F`rF3F:-F$6%7$FG7$F\\qF+-F46&F6F*F*F*-F;6#F)-F$6%7$Fds7$$ \"1YN$****R;s%F-$\"11\"\\&fw_oLF-FesFgs-F$6%7$Fds7$$\"1%*3XSBZJYF-$\"1 bk1++OyKF-FesFgs-F$6%7$7$$\"1$[uRj\")R&yF`r$\"\")F*7$$\"1'>A>qhbw'F`r$ \"1u'e-<;\\&zF-FUF:-F$6%7$7$F*F_uF\\uFUF:-F$6%7$F\\u7$Fbu$\"1E8uHQ3X!) F-FUF:-F$6%7$7$$!1U([8'*GI/#F-Ffp7$$!1rRba4(=:#F-$\"1;v[a4^toF-FUF:-F$ 6%7$Fcv7$Fgv$\"1k[+&HVLy'F-FUF:-F$6%7$7$$!1!>YZ7F%GGF-FfpFcvFUF:-F$6%7 $Fep7$$\"1MMTbc=pTF-FcoFesFgs-F$6%7$Fjw7$$\"1xH+p;]^RF-FcoFesFgs-F$6%7 $Fjw7$$\"1!)oYK)f_,%F-$\"1\\HU!e#*pU'F-FesFgs-F$6%7$7$$!1_DgO=g9KF-F(7 $$!1!y2)HQWBLF-F/FUF:-F$6%7$F^y7$FbyFBFUF:-F$6%7$7$$!\"%F*F(F^yFUF:-F$ 6%7$7$$\"1VQ(3#\\YeIF-F^r7$$\"1S*4uv1Z*HF-$\"1m\"zWr1(*z'F`rFesFgs-F$6 %7$FZFazFesFgs-F$6%7$Faz7$Fbz$\"1fmmu;!Q1(F`rFesFgs-F$6%7$7$FdvFN7$Fgv F[oFUF:-F$6%7$Fe[l7$FgvFSFUF:-F$6%7$7$FewFNFe[lFUF:-F$6%7$7$$!1&RwuvmI F#F-$\"1&)f,#\\(y$Q(F-7$$!1B;o](3>Q#F-$\"1fYFiOqQtF-F3F:-F$6%7$Fb\\l7$ $!1?x@(e]\"=BF-$\"1d2\"))\\X\\F(F-F3F:-F$6%7$FdwFb\\lF3F:-F$6%7$7$$!1$ [uRj\")R&yF`rF*7$$!1'>A>qhbw'F`r$!1'fKT(HQ3X!# " 0 "" {MPLTEXT 1 0 39 "display(tot.(0..npts),insequence=tr ue);" }}{PARA 13 "" 1 "" {INLPLOT "6#-%(ANIMATEG6*7,-%'CURVESG6%7$7$$ \"\"%\"\"!$\"1_DgO=g9K!#:7$$\"1E8uHQ3XSF1$\"1!y2)HQWBLF1-%'COLOURG6&%$ RGBG$\"*++++\"!\")F.F.-%*THICKNESSG6#\"\"#-F(6%7$F+7$$\"1u'e-<;\\&RF1F 5F7F>-F(6%7$7$F,F,F+F7F>-F(6%7$7$$\"1[uRj\")R&y%F1F,7$$\"1?A>qhbwYF1F3 -F86&F:F.F;F.F>-F(6%7$FO7$FSFFFUF>-F(6%7$FKFOFUF>-F(6%7$FK7$FPF/-F86&F :F.F.F.-F?6#F--F(6%7$F[o7$$\"1YN$****R;s%F1$\"11\"\\&fw_oLF1F\\oF^o-F( 6%7$F[o7$$\"1%*3XSBZJYF1$\"1bk1++OyKF1F\\oF^o-%(SCALINGG6#%,CONSTRAINE DG7,-F(6%7$7$$\"1RO9)GDQh$F1$\"15QDvGdr6F17$$\"15%Q\\H$)\\]$F1$\"1%[7b /*[E6F1FUF>-F(6%7$7$$\"1!>YZ7F%GGF1F[qFhpFUF>-F(6%7$Fhp7$F^q$\"1O^*\\q cm@\"F1FUF>-F(6%7$Feq7$$\"1&RwuvmIF#F1$\"1R,%)z]7ih!#;F7F>-F(6%7$Far7$ $\"1B;o](3>Q#F1$\"1*R`sPjHh'FfrF7F>-F(6%7$Far7$$\"1?x@(e]\"=BF1$\"1DC* =,X0D(FfrF7F>-F(6%7$7$$\"1VQ(3#\\YeIF1Fdr7$$\"1S*4uv1Z*HF1$\"1m\"zWr1( *z'FfrF\\oF^o-F(6%7$FeqFjsF\\oF^o-F(6%7$Fjs7$F[t$\"1fmmu;!Q1(FfrF\\oF^ oF`p7*-F(6%7$7$$!1$[uRj\")R&yFfrF.7$$!1'>A>qhbw'Ffr$!1'fKT(HQ3X!# -F(6%7$F_u7$Fcu$\"1'fKT(HQ3XFguF7F>-F(6%7$7$F.F.F_uF7F>-F(6%7$Fav7$$\" 1$[uRj\")R&yFfrF.FUF>-F(6%7$Fev7$$\"1'>A>qhbw'FfrF\\vFUF>-F(6%7$Fev7$F \\wFeuFUF>-F(6%7$FavFavF\\oF^oF`p7,-F(6%7$7$$!1U([8'*GI/#F1F[q7$$!1rRb a4(=:#F1F\\rFUF>-F(6%7$Fiw7$F]xF`qFUF>-F(6%7$7$$!1!>YZ7F%GGF1F[qFiwFUF >-F(6%7$7$$!1')f,#\\(y$Q$F1$\"10O_UK$ps\"F17$$!1gYFiOqQLF1$\"1x$=$\\74 =;F1F7F>-F(6%7$F\\y7$$!1d2\"))\\X\\F$F1$\"1!G#y7%\\=o\"F1F7F>-F(6%7$Ff xF\\yF7F>-F(6%7$7$$!1Q&='G$*Q)f#F1F_y7$$!1TC3#\\Z@m#F1$\"1.(f!z]-F(6%7$Fi[l7$F]\\lFFFUF>- F(6%7$7$$!\"%F.F,Fi[lFUF>-F(6%7$Ff\\l7$Fg\\lFPF7F>-F(6%7$F\\]l7$$!1u'e -<;\\&RF1FSF7F>-F(6%7$F\\]l7$$!1E8uHQ3XSF1FSF7F>-F(6%7$7$Fj[lFP7$$!11 \"\\&fw_oLF1FdoF\\oF^o-F(6%7$F\\^l7$$!1bk1++OyKF1F\\pF\\oF^o-F(6%7$Ff \\lF\\^lF\\oF^oF`p7,-F(6%7$7$Fjw$\"1!>YZ7F%GoF17$F]x$\"1;v[a4^toF1FUF> -F(6%7$F]_l7$F]x$\"1k[+&HVLy'F1FUF>-F(6%7$7$FgxF^_lF]_lFUF>-F(6%7$7$$! 1&RwuvmIF#F1$\"1&)f,#\\(y$Q(F17$$!1B;o](3>Q#F1$\"1fYFiOqQtF1F7F>-F(6%7 $F``l7$$!1?x@(e]\"=BF1$\"1d2\"))\\X\\F(F1F7F>-F(6%7$F\\`lF``lF7F>-F(6% 7$7$$!1Y*ySfow[\"F1Fc`l7$$!1/%*[!e_`q\"F1Fc`lF\\oF^o-F(6%7$Fhal7$$!1,b --F(6%7$7$F.F^clF]clFUF>-F(6%7$F]cl7 $F\\w$\"1E8uHQ3X!)F1FUF>-F(6%F\\clF7F>-F(6%FeclF7F>-F(6%FiclF7F>-F(6%7 $7$$\"1(*[zEjzq:F1F^cl7$$\"1RWQSB6`8F1$\"1[t^SB$)4zF1F\\oF^o-F(6%7$Ffc lFfdlF\\oF^o-F(6%7$Ffdl7$Fjdl$\"1`E[fw;!4)F1F\\oF^oF`p7,-F(6%7$7$$\"1' )f,#\\(y$Q$F1$\"1&RwuvmIF'F17$$\"1gYFiOqQLF1$\"1B;o](3>Q'F1F7F>-F(6%7$ F[fl7$$\"1d2\"))\\X\\F$F1$\"1@x@(e]\"=jF1F7F>-F(6%7$7$FfqF^_lF[flF7F>- F(6%7$F`gl7$$\"1MMTbc=pTF1F^flF\\oF^o-F(6%7$Fdgl7$$\"1xH+p;]^RF1F^flF \\oF^o-F(6%7$Fdgl7$$\"1!)oYK)f_,%F1$\"1\\HU!e#*pU'F1F\\oF^o-F(6%7$7$Fi pF^_l7$F^qFa_lFUF>-F(6%7$Fhhl7$F^qFg_lFUF>-F(6%7$F`glFhhlFUF>F`p" 2 413 413 413 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 231 188 1 0 0 0 511 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 7 }{VIEWOPTS 1 1 0 1 1 1803 }