{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warni ng" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 268 "restart:\nwith(lina lg):\nMM:=omega->matrix(3,3,[1,0,0,0,cos(omega),-sin(omega),0,sin(omeg a),cos(omega)]):\nomega:=Pi/4:R:=4:r:=1:\nomega:=Pi/3:R:=1:r:=2:\np:=1 : # pour pr\351ciser le nombre de tours \340 effectuer\nn:=25 : # le nombre de positions du cercle mobile" }}{PARA 7 "" 1 " " {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 945 "# Je fabrique la matrice de la rotation vectorielle \+ d'axe la tangente au cercle fixe\nP:=t->matrix(3,3,[-sin(t),-cos(t),0, cos(t),-sin(t),0,0,0,1]):\nM:=t->evalm(P(t)&*MM(omega)&*inverse(P(t))) :\n# On conna\356t l'image de O dans la rotation affine\nrota:=(x,y,z) ->op(convert((evalm(M(t)&*vector([x,y,z])+vector([R*(1-cos(omega))*cos (t),R*(1-cos(omega))*sin(t),R*sin(omega)]))),list)):\n\n#cercles:=seq( tubeplot([rota((R-r)*cos(t)+r*cos(t-u),(R-r)*sin(t)+r*sin(t-u),0),u=0. .2*Pi,radius=#0.05],color=black),t=seq(k*p*2*Pi/n,k=0..n-1)):\ncercles :=seq(polygonplot3d([seq([rota((R-r)*cos(t)+r*cos(t-u),(R-r)*sin(t)+r* sin(t-u),0)],u=seq(k*2*Pi/n,k=0..n-1))],color=white),t=seq(k*p*2*Pi/n, k=0..n-1)):\ncerclefixe:=spacecurve([R*cos(v),R*sin(v),0,v=0..2*Pi],co lor=blue,thickness=2):\n\ncyclosph:=spacecurve([rota((R-r)*cos(t)+r*co s(t-R/r*t),(R-r)*sin(t)+r*sin(t-R/r*t),0),t=0..2*p*Pi],numpoints=400,c olor=red):\n\nh:=(r-R*cos(omega))/sin(omega):\nRho:=sqrt(R**2+h**2):\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 201 "h:=(r-R*cos(omega))/si n(omega):\nRho:=sqrt(R**2+h**2):\nsphere:=plot3d([Rho*cos(a)*cos(b)*.9 7,Rho*cos(a)*sin(b)*.97,Rho*sin(a)*.97+h],a=-Pi/2..Pi/2+arctan(R/h),b= 0..2*Pi,style=patchnogrid,grid=[50,50]):\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 185 "segm ents:=seq(\nspacecurve(\n[[rota((R-r)*cos(t),(R-r)*sin(t),0)],[rota((R -r)*cos(t)+r*cos(t-R/r*t),(R-r)*sin(t)+r*sin(t-R/r*t),0)]],color=black ,thickness=2),\nt=seq(k*2*p*Pi/n,k=0..n-1)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "display([cerclefixe,sphere,cyclosph,display([ce rcles],insequence=true),display([segments],insequence=true)],orientati on=[77,71]);" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT3D 292 283 283 {PLOTDATA 3 "6$-%(ANIMATEG6;7'-%)POLYGONSG6$7;7%$\"\"\"\"\"!$F.F.F/7%$ \"+6;$eo*!#5$!+Wxzt\\F3$\"*:c:W&F37%$\"++o1j()F3$!+#[t]j*F3$\"+]6VU@F3 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