{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 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 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 "Heading 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 Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 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 "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 43 "bielle de B\351rard et mouvement plan su r plan" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Mail de Ferr\351ol du 3 1/01/2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 741 "Bonsoir,\n\npour changer des abondants, j'ai repris un pb que j'a vais mis de c\364t\351 depuis plusieurs mois :\n\nd\351terminer la bas e et la roulante du mouvement de la bielle\nhttp://www.mathcurve.com/c ourbes2d/bielledeberard/bielledeberard.shtml\n\ndans le fichier joint, j'ai un petit ennui, car j'ai deux courbes diff\351rentes quand la bi elle est \340 droite de la manivelle et quand elle est \340 gauche ; a urais tu une id\351e pour les r\351unir ?\n\ncet exemple est tr\350s i nt\351ressant car on obtient exactement comme base la roulante de cell e du mouvement concho\357dal circulaire, et comme roulante sa base\n\n voir au bas de :\nhttp://www.mathcurve.com/courbes2d/conchoiddecercle/ conchoiddecercle.shtml\n\nc'est une constatation de calcul, mais certa inement pas fortuit...\n" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 " Pro gramme 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)-0.0 00001:" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords \+ has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 176 "om ega:=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)->omega(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->complexplot(m(u),u=-angle..t) :\nroulante:=t->complexplot(m2(t,u),u=-angle..angle,color=magenta):\ns egment:=t->display(complexplot([m(t),m2(t,0),omega(t),0],color=black)) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "animation:=display(se q(display(segment(t),roulante(t),display([roulette1(t),roulette2(t)],t hickness=2)),t=seq(k*angle/n+0.0000001,k=-n..n)),insequence=true):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "display(base,display([roul ette1(angle),roulette2(angle)],linestyle=2),animation,scaling=constrai ned,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*si n(t)/sqrt(1-b^2*sin(t)^2))+Pi:\nm1:=omega+I*D(omega)/D(theta):\nm2:=(t ,u)->omega(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*the ta(t-alpha)):m(t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "base :=complexplot(m1(t),t=-angle..angle,color=blue):\nroulette1:=t->comple xplot(m(u),u=-angle..t):\nroulante:=t->complexplot(m2(t,u),u=-angle..a ngle,color=magenta):\nsegment:=t->display(complexplot([m(t),m2(t,0),om ega(t),0],color=black)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "animation:=display(seq(display(segment(t),roulante(t),display([ro ulette1(t),roulette2(t)],thickness=2)),t=seq(k*angle/n+0.0000001,k=-n. .n)),insequence=true):" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "display (base,display([roulette1(angle),roulette2(angle)],linestyle=2),animati on,scaling=constrained,axes=none);" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 50 " pg qui marche avec un s\351v\350 re bricolage ( ;-(( !" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "r estart:\nwith(plots):\nb:=2.: a:=0: alpha:=0: alpha2:=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)/sqrt(1-b^2*sin(t)^2)):\nm11: =omega+I*D(omega)/D(theta):\nm21:=(t,u)->omega(t)+I*exp(I*(theta(t)-th eta(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=bl ue):\nroulette11:=t->complexplot(m1(u),u=-angle..t,color=COLOR(RGB,0,0 .8,0)):\nroulette21:=t->complexplot(omega(u),u=-angle..t,color=COLOR(R GB,0,0.8,0)):\nroulante1:=t->complexplot(m21(t,u),u=-angle..angle,colo r=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->arctan(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*exp(I*theta1(t-alpha)):m(t):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 374 "base2:=complexplot(m12(t),t=-angle ..angle,color=blue):\nroulette12:=t->complexplot(m2(-u),u=-angle..t,co lor=COLOR(RGB,0,0.8,0)):\nroulette22:=t->complexplot(omega(-u),u=-angl e..t,color=COLOR(RGB,0,0.8,0)):\nroulante2:=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*(the ta(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,color=magenta):\nroulante4:=t ->c omplexplot(m24(t,u),u=-angle..angle,color=magenta):" }}{PARA 7 "" 1 " " {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "animation1:=seq(display(se gment1(t),roulante1(t),roulante4(t),\n display([roulette11(t),roulette 21(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 "#,ro ulette21(angle) ### on efface la trace de la manivelle\nanimation2:=se q(display(display([roulette11(angle)],thickness=2),\n segme nt2(-t),roulante3(t),roulante2(-t),\n display([roulette12(t),ro ulette22(t)],thickness=2)),t=seq(k*angle/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,animation2],insequence=true),scalin g=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 0 {PARA 3 "" 0 "" {TEXT -1 22 " Pg un peu p lus propre" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 887 "cart:= z ->[Re(z),Im(z)]:\nwith(pl ots):\nb:=1.:# longueur de la manivelle OA\nL:=0.5*b:\nL1:=1.2*b:\n### ## on s'int\351resse \340 la trajectoire de C de AB tel que AC=L1\n n :=10:\n if L>=b then angle:=Pi/2:vue:=view=[-(b+L1)..b+L1,-(b+L1)..b+L 1]:\n else angle:=arcsin(L/b): vue:=NULL: fi:\n#-----extr\351m it\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):\ntheta 2:=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*(t heta(t)-theta(u)) )*D(omega)(u)/D(theta)(u)):\n#------ point courant d e la base ------------- \nmB:= theta -> omega+I*D(omega)/D(theta):\n#- ---------- extremit\351 de la bielle ---------- " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "mE:=(t,theta) ->omega(t)+L1*exp(I*theta(t)):\n#----- -------- point du tiroir de la bielle----\nmL:=(t,theta) -> omega(t)+e xp(I*theta(t))*L:\n#--------------- base 1------------------------- " 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