{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 "Headi ng 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -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 }{PSTYLE "Tit le" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 43 "bielle de B\351rard et mo uvement plan sur plan" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Mail de \+ Ferr\351ol du 31/01/2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 741 "Bonsoir,\n\npour changer des abondants, j'ai repr is un pb que j'avais mis de c\364t\351 depuis plusieurs mois :\n\nd \351terminer la base et la roulante du mouvement de la bielle\nhttp:// www.mathcurve.com/courbes2d/bielledeberard/bielledeberard.shtml\n\ndan s le fichier joint, j'ai un petit ennui, car j'ai deux courbes diff \351rentes quand la bielle est \340 droite de la manivelle et quand el le est \340 gauche ; aurais tu une id\351e pour les r\351unir ?\n\ncet exemple est tr\350s int\351ressant car on obtient exactement comme ba se la roulante de celle du mouvement concho\357dal circulaire, et comm e roulante sa base\n\nvoir au bas de :\nhttp://www.mathcurve.com/courb es2d/conchoiddecercle/conchoiddecercle.shtml\n\nc'est une constatation de calcul, mais certainement pas fortuit...\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 29 " Programme initial de Ferr\351ol" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 72 "restart:b:=2.:a:=0:alpha:=0:alpha2:=0:n:=10: angle:=arcsin(1/b)-0.000001:" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, \+ the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 176 "omega:=t->b*exp(I*t):\ntheta:=t->-arctan(b*sin(t)/ sqrt(1-b^2*sin(t)^2)):\nm1:=omega+I*D(omega)/D(theta):\nm2:=(t,u)->ome ga(t)+I*exp(I*(theta(t)-theta(u)))*D(omega)(u)/D(theta)(u):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "m:=t->omega(t)+b*exp(I*theta (t-alpha)):m(t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "base:= complexplot(m1(t),t=-angle..angle,color=blue):\nroulette1:=t->complexp lot(m(u),u=-angle..t):\nroulante:=t->complexplot(m2(t,u),u=-angle..ang le,color=magenta):\nsegment:=t->display(complexplot([m(t),m2(t,0),omeg a(t),0],color=black)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 " animation:=display(seq(display(segment(t),roulante(t),display([roulett e1(t),roulette2(t)],thickness=2)),t=seq(k*angle/n+0.0000001,k=-n..n)), insequence=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "displ ay(base,display([roulette1(angle),roulette2(angle)],linestyle=2),anima tion,scaling=constrained,axes=none);" }}{PARA 13 "" 1 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "omega:=t->b*exp(I*t): \ntheta:=t->arctan(b*sin(t)/sqrt(1-b^2*sin(t)^2))+Pi:\nm1:=omega+I*D(o mega)/D(theta):\nm2:=(t,u)->omega(t)+I*exp(I*(theta(t)-theta(u)))*D(om ega)(u)/D(theta)(u):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "m:= t->omega(t)+b*exp(I*theta(t-alpha)):m(t):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 235 "base:=complexplot(m1(t),t=-angle..angle,color=blue ):\nroulette1:=t->complexplot(m(u),u=-angle..t):\nroulante:=t->complex plot(m2(t,u),u=-angle..angle,color=magenta):\nsegment:=t->display(comp lexplot([m(t),m2(t,0),omega(t),0],color=black)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "animation:=display(seq(display(segment(t),ro ulante(t),display([roulette1(t),roulette2(t)],thickness=2)),t=seq(k*an gle/n+0.0000001,k=-n..n)),insequence=true):" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "display(base,display([roulette1(angle),roulette2(ang le)],linestyle=2),animation,scaling=constrained,axes=none);" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 50 " pg qui marc he avec un s\351v\350re bricolage ( ;-(( !" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "restart:\nwith(plots):\nb:=2.: a:=0: alpha:=0: alp ha2:=0: n:=10: angle:=arcsin(1/b)-0.000001:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "omega:=t->b*exp(I*t):\ntheta:=t->-arctan(b*sin(t)/sq rt(1-b^2*sin(t)^2)):\nm11:=omega+I*D(omega)/D(theta):\nm21:=(t,u)->ome ga(t)+I*exp(I*(theta(t)-theta(u)))*D(omega)(u)/D(theta)(u):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "m1:=t->omega(t)+b*exp(I*theta(t-alpha)):m (t):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 344 "base1:=complexplot(m11(t), t=-angle..angle,color=blue):\nroulette11:=t->complexplot(m1(u),u=-angl e..t,color=COLOR(RGB,0,0.8,0)):\nroulette21:=t->complexplot(omega(u),u =-angle..t,color=COLOR(RGB,0,0.8,0)):\nroulante1:=t->complexplot(m21(t ,u),u=-angle..angle,color=magenta):\nsegment1:=t->display(complexplot( [m1(t),m21(t,0),omega(t),0],color=black)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "theta1:=t->arc tan(b*sin(t)/sqrt(1-b^2*sin(t)^2))+Pi:\nm12:=omega+I*D(omega)/D(theta1 ):\nm22:=(t,u)->omega(t)+I*exp(I*(theta1(t)-theta1(u)))*D(omega)(u)/D( theta1)(u):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "m2:=t->omega(t)+b*ex p(I*theta1(t-alpha)):m(t):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 374 "base 2:=complexplot(m12(t),t=-angle..angle,color=blue):\nroulette12:=t->com plexplot(m2(-u),u=-angle..t,color=COLOR(RGB,0,0.8,0)):\nroulette22:=t- >complexplot(omega(-u),u=-angle..t,color=COLOR(RGB,0,0.8,0)):\nroulant e2:=t->complexplot(m22(t,u),u=-angle..angle,color=magenta):\nsegment2: =t->display(complexplot([m2(t),m22(t,0),omega(t),0],color=black)):\n#= == suite pas terrible !!!" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 292 "m23:= (t,u)->omega(-t)-I*exp(I*(theta(t)-theta(u)))*D(omega)(u)/D(theta)(u): \nm24:=(t,u)->omega(t)-I*exp(-I*(theta1(t)-theta1(u)))*D(omega)(-u)/D( theta1)(-u):\nroulante3:=t ->complexplot(m23(t,u),u=-angle..angle,colo r=magenta):\nroulante4:=t ->complexplot(m24(t,u),u=-angle..angle,color =magenta):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoo rds has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "animation1:=seq(display(segment1(t),roulante1(t),roulante4(t),\n \+ display([roulette11(t),roulette21(t)],thickness=2)),t=seq(k*angle/n+0. 0000001,k=-n..n)):#" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 275 "#,roulette21(angle) ### on efface la trace \+ de la manivelle\nanimation2:=seq(display(display([roulette11(angle)],t hickness=2),\n segment2(-t),roulante3(t),roulante2(-t),\n \+ display([roulette12(t),roulette22(t)],thickness=2)),t=seq(k*angl e/n+0.0000001,k=-n..n)):#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "display(base1,base2,display([roulette11(angle),roulette12(angle), roulette22(angle)],linestyle=2),\n display([animation1,ani mation2],insequence=true),scaling=constrained,axes=none);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 22 " Pg un peu plus propre" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 900 "cart:= z ->[Re(z),Im(z)]:\nwith(plots):\nb:=1.:# longueur de la manivelle OA \nL:=b*0.9:\nL1:=1.2*b:\n##### L=longueur de la bielle jusqu'au tiroir B, B d\351crit Ox\n##### on s'int\351resse \340 la trajectoire de C d e AB tel que AC=L1 \n n:=10: \nangle:=arcsin(L/b):# arctan(1/sqrt(b*b -1)):#arcsin(1/b)-0.000001:\n#-----extr\351mit\351 de la manivelle ou \+ origine de la bielle\nomega:=t ->b*(cos(t)+I*sin(t)):\n#-------------- ---------------- \n####theta:=t-> -arctan(b*sin(t)/sqrt(1-b^2*sin(t)^2 )):\ntheta1:=t-> -arcsin(b*sin(t)/L):\ntheta2:=t-> Pi+arcsin(b*sin(t)/ L):\n#----- pt courant de la roulante ------\nmR:=(t,u,theta) -> omega (t)+I*exp( I*(theta(t)-theta(u)) )*D(omega)(u)/D(theta)(u):\nmRcomp:=( t,u,theta) -> omega(t)+I*conjugate(exp( I*(theta(t)-theta(u)) )*D(omeg a)(u)/D(theta)(u)):\n#------ point courant de la base ------------- \n mB:= theta -> omega+I*D(omega)/D(theta):\n#----------- extremit\351 de la bielle ---------- " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "mE:=(t,t heta) ->omega(t)+L1*exp(I*theta(t)):\n#------------- point du tiroir d e la bielle----\nmL:=(t,theta) -> omega(t)+exp(I*theta(t))*L:\n#------ --------- base 1------------------------- " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "base:=theta ->complexplot((mB(theta))(t),t=-angle..an gle,color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 893 "#------------- roulante --------------\nroulante:=(t,theta) ->complexplot(mR(t,u,the ta),u=-angle..angle,color=magenta):\nroulantecomp:=(t,theta) ->complex plot(mRcomp(t,u,theta),u=-angle..angle,color=magenta):\n#------------ \+ roulette extremit\351 ---------------------\nroulette1:=(t,theta)->com plexplot(mE(u,theta),u=-angle..t,color=COLOR(RGB,0,0.8,0)):\nroulette1 comp:=(t,theta)->complexplot(mEcomp(u,theta),u=-angle..t,color=COLOR(R GB,0,0.8,0)):\n#------------ roulette du point du tiroir de la bielle \+ ---------------------\nrouletteL:=(t,theta)->complexplot(mL(u,theta),u =-angle..t,color=COLOR(RGB,0,0,1)):\n#------------ roulette de l'origi ne de la bielle ---------------------\nroulette2:=t->complexplot(omega (u),u=-angle..t,color=COLOR(RGB,1,0,0)):\n#--------------------------- -----------------------------------------\nsegment1:=(t,theta)->displa y(complexplot([mE(t,theta),omega(t),0],color=black)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 184 "fixe:=display([base(theta1),roulet te1(angle,theta1),roulette1(angle,theta2),\n roulette2(a ngle),rouletteL(angle,theta1),rouletteL(angle,theta2),base(theta2)],li nestyle=3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 727 "w:=k ->k*angle/n+0. 000001:\nmobile:=display([seq(display([\n roulan tecomp(w(k),theta2),\n pointplot(map(cart,[mL(w( k),theta1),mE(w(k),theta1),omega(w(k))])\n \+ ,symbol=circle,symbolsize=14),\n roulant e(w(k),theta1),segment1(w(k),theta1)\n ]),k=-n..n )\n ,seq(display([\n roulantecomp (-w(k),theta1),\n pointplot(map(cart,[mL(-w(k),t heta2),mE(-w(k),theta2),omega(-w(k))])\n \+ ,symbol=circle,symbolsize=14),\n roulante(- w(k),theta2),segment1(-w(k),theta2)\n ]),k=-n..n) \n],insequence=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "t t:=cat(\"OA=\",convert(evalf(b,2),string), \", AB=\",convert(evalf(L,2 ),string), \" , BC=\",convert(evalf(L1-L,2),string)):\ndisplay([fixe,m obile],scaling=constrained,axes=none,title=tt);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 16 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }