{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 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 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 "" {MPLTEXT 1 0 246 "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:\nR:=4:r:=1:\np:=1: # pour pr \351ciser le nombre de tours \340 effectuer\nn:=25: # le nombr e de positions du cercle mobile" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1056 "# 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(con vert((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,ra dius=#0.05],color=black),t=seq(k*p*2*Pi/n,k=0..n-1)):\ncercles:=seq(po lygonplot3d([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],color=blue ,thickness=2):\n\ncyclosph:=spacecurve([rota((R-r)*cos(t)+r*cos(t-R/r* t),(R-r)*sin(t)+r*sin(t-R/r*t),0),t=0..2*p*Pi],numpoints=400,color=red ):\n\nh:=(r-R*cos(omega))/sin(omega):\nRho:=1.01*sqrt(R**2+h**2):\nsph ere:=plot3d([Rho*cos(a)*cos(b),Rho*cos(a)*sin(b),Rho*sin(a)+h],a=0..Pi /2,b=0..2*Pi,style=patchnogrid):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 185 "segments:=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 0 151 "display([cerclefixe,sphere ,cyclosph,display([cercles],insequence=true),display([segments],insequ ence=true)],scaling=constrained,orientation=[-45,168]);" }}{PARA 13 " " 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6%-%(ANIMATEG6;7'-%)POLYGONS G6$7;7%$\"\"%\"\"!F.F.7%$\"+S\\yxR!\"*$!+s))*o[#!#5$\")g]@AF27%$\"+:c` 7RF2$!+Tn`<[F5$\")&Qku)F27%$\"+z=N3QF2$!+g5ZXoF5$\"*@\"[;>F27%$\"+z*z< n$F2$!+a#zKW)F5$\"*@+AG$F27%$\"+K7S6NF2$!+g^c5&*F5$\"*o()f)[F27%$\"+@G HPLF2$!+%Gn-)**F5$\"*zrqi'F27%$\"+@YRgJF2$!+3D(G#)*F5$\"*z`gR)F27%$\"+ &z@=*HF2$!+B0F[!*F5$\"+0#y\"35F27%$\"+%Rm@%GF2$!+GC80xF5$\"+1O$y:\"F27 %$\"+<=$3s#F2$!+?D&y(eF5$\"+$=o\"z7F27%$\"+h>WNEF2$!+FbC\"o$F5$\"+R!eX O\"F27%$\"+(=i8f#F2$!+OBL`7F5$\"+8yj39F27%Fip$\"+OBL`7F5F]q7%Fbp$\"+Fb C\"o$F5Ffp7%F[p$\"+?D&y(eF5F_p7%Fdo$\"+GC80xF5Fho7%F]o$\"+B0F[!*F5Fao7 %Ffn$\"+3D(G#)*F5Fjn7%FU$\"+%Gn-)**F5FY7%FN$\"+g^c5&*F5FR7%FG$\"+a#zKW 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