{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 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 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 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 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 " Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 0 0 0 0 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 Out put" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 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 "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 18 "" 0 "" {TEXT -1 85 " Spire d'axe oy de rayon \+ a du plan xOz\nlignes de champ et niveau du champ magn\351tique" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 " Champ magn\351tique dans le pla n xOy : \nBx = " }{XPPEDIT 18 0 "mu*I*a/2/Pi;" "6#*,%#muG\"\"\"%\"IGF% %\"aGF%\"\"#!\"\"%#PiGF)" }{TEXT -1 1 " " }{XPPEDIT 18 0 "Int((x*cos(t )-a)/(((x-a*cos(t))^2+y^2)^(3/2)),t = 0 .. Pi);" "6#-%$IntG6$*&,&*&%\" xG\"\"\"-%$cosG6#%\"tGF*F*%\"aG!\"\"F*),&*$,&F)F**&F/F*-F,6#F.F*F0\"\" #F**$%\"yGF8F**&\"\"$F*F8F0F0/F.;\"\"!%#PiG" }{TEXT -1 18 " ; \+ By = " }{XPPEDIT 18 0 "mu*I*a/2/Pi;" "6#*,%#muG\"\"\"%\"IGF%%\"aGF% \"\"#!\"\"%#PiGF)" }{TEXT -1 1 " " }{XPPEDIT 18 0 "Int(-y*cos(t)/(((x- a*cos(t))^2+y^2)^(3/2)),t = 0 .. Pi);" "6#-%$IntG6$,$*(%\"yG\"\"\"-%$c osG6#%\"tGF)),&*$,&%\"xGF)*&%\"aGF)-F+6#F-F)!\"\"\"\"#F)*$F(F8F)*&\"\" $F)F8F7F7F7/F-;\"\"!%#PiG" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "evalf(int(x*y,x=0..1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&$\"+++++]!#5\"\"\"%\"yGF(F(" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 40 "calculs pr\351liminaires \340 ne pas ex\351cuter " } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "a:=1:\nBX:=int(-y*cos(t)/( x^2+y^2+a^2-2*x*a*cos(t))^(3/2),t=0..Pi):\nBY:=int((x*cos(t)-a)/(x^2+y ^2+a^2-2*x*a*cos(t))^(3/2),t=0..Pi):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "BX1:=sort(subs(EllipticK(2*sqrt(x/(x^2+y^2+1+2*x)))=KK,Elliptic E(2*sqrt(x/(x^2+y^2+1+2*x)))=EE,BX),KK);" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 334 " BY1:=sort(subs(EllipticK(2*sqr t(x/(x^2+y^2+1+2*x)))=KK,EllipticE(2*sqrt(x/(x^2+y^2+1+2*x)))=EE,BY),K K);\n\n BX1 := ((x^2+y^2+1-2*x )*KK-(x^2+y^2+1)*EE)/\n (x^ 2+y^2+1+2*x)^(1/2)/(x^2+y^2+1-2*x);\n BY1 := ( -(x^2+y^2-2*x+1 )*KK+( x^2+y^2-1)*EE)/\n (x^2+y^2+1+2*x)^(1/2)*y/(x^2+y^2+1-2*x)/x ;\n theta:=arctan(BY1/BX1);" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, \+ computation interrupted\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 22 " programmes des trac\351s " }}{PARA 0 "" 0 "" {TEXT -1 111 "Principe : au point courant P, je tr ace le point suivant Q tel que PQ = pas*[BX,BY] o\371 [BX,BY] est un v ecteur \"" }{TEXT 256 10 "\340 peu pr\350s" }{TEXT -1 1 " " }{TEXT 257 14 "et au mieux(?)" }{TEXT -1 41 " de norme 1 et colin\351aire\" a u champ en P." }}{PARA 0 "" 0 "" {TEXT -1 111 "J'ai essay\351 d'adapte r le pas pour optimiser( intuitivement : plus \"\347a tourne\", plus i l faut diminuer le pas ). " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "with(plots):\nBx :=(x,y) -> +((x^2+y^2+1-2*x)*EllipticK(2*sqrt(x/(x^2+y^2+1+2*x)))-(x^ 2+y^2+1)*\n EllipticE(2*sqrt(x/(x^2+y^2+1+2*x))))/(x^2+y^2+1+2*x)^ (1/2)*y/(x^2+y^2+1-2*x)/x:\nBy := (x,y) -> (-(x^2+y^2+1-2*x)*EllipticK (2*sqrt(x/(x^2+y^2+1+2*x)))+(-1+x^2+y^2)*\n EllipticE(2*sqrt(x/ (x^2+y^2+1+2*x))))/(x^2+y^2+1+2*x)^(1/2)/(x^2+y^2+1-2*x):" "6#C%-%%wit hG6#%&plotsG>%#BxGf*6$%\"xG%\"yG7\"6$%)operatorG%&arrowG6\"*,,&*&,**$F ,\"\"#\"\"\"*$F-F8F9F9F9*&F8F9F,F9!\"\"F9-%*EllipticKG6#*&F8F9-%%sqrtG 6#*&F,F9,**$F,F8F9*$F-F8F9F9F9*&F8F9F,F9F9F%#ByGf*6$F,F-7\"6$F0F1F2*(,&*& ,**$F,F8F9*$F-F8F9F9F9*&F8F9F,F9F6#*&F8F9-FB6#*&F,F9,**$F,F8F9*$ F-F8F9F9F9*&F8F9F,F9F9F " 0 "" {MPLTEXT 1 0 312 "\n\ntheta := (x,y) -> -arcta n((x*(-(x^2+y^2+1-2*x)*EllipticK(2*sqrt(x/(x^2+y^2+1+2*x)))+\n \+ (-1+x^2+y^2)*EllipticE(2*sqrt(x/(x^2+y^2+1+2*x)))))/(((x^2+y^2+1-2*x) *\n EllipticK(2*sqrt(x/(x^2+y^2+1+2*x)))-(x^2+y^2+1)*\n \+ EllipticE(2*sqrt(x/(x^2+y^2+1+2*x))))*y)) :\n normE:= (x,y) -> sqrt( x^2+y^2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1968 "# ================== ===================================\n# ligne de champ coupant l'axe de s x \340 l'abscisse x0\n# -------------------------------------------- ---------\nlig_champ:=proc(x0) \n global Bx,By,theta;\n local \+ i,liste, xi,yi,xip,yip,t,ti,ttamp,X,Y,X1,Y1,NN,NN1, pi,pas,delta:\n \+ pas:=0.01:\n xi:=x0;yi:=0.00001; ti:=theta(xi,yi); \n t:=0; \+ liste:=[xi,yi]; pi:=evalf(Pi):\n for i while t <=pi and i<2000 do \n X:=Bx(xi,yi): Y:=By(xi,yi):NN:=normE(X,Y):\n xip: =xi+pas*X/NN; yip:=yi+pas*Y/NN;\n X1:=Bx(xip,yip): Y1:=By(xip ,yip):NN1:=normE(X1,Y1):\n xi:=xi+pas*(X/NN+X1/NN1)/2;\n \+ yi:=yi+pas*(Y/NN+Y1/NN1)/2;\n liste:=[xi,-yi],liste,[xi, yi]:\n ttamp:=theta(xi,yi):\n delta:=min(abs(ttamp-t i),abs(pi-abs(ttamp-ti))) :\n t:=t+delta:\n if delt a<0.01 then pas:=2*pas #and pas < 0.5\n elif delta>0.04 t hen pas:=pas/2 fi;# and pas > 0.05\n ti:=ttamp:\n od;\nev alf([liste]):\nend:\n\n# ============================================= ========\n# ligne de niveau coupant l'axe des y \340 l'abscisse y0\n# \+ -----------------------------------------------------\nlig_niv:=proc(y 0) \n global Bx,By,theta;\n local i,liste, xi,yi,xip,yip,t,ti, ttamp,X,Y,X1,Y1,NN,NN1, pi,pas,delta:\n pas:=0.01:\n\n pi:=eva lf(Pi): xi:=0.0001;yi:=y0; ti:=theta(xi,yi); \n t:=0; liste:=[xi,y i]; \n for i from 1 while t <=pi and i<1000 do\n X:=By( xi,yi): Y:=Bx(xi,yi): NN:=normE(X,Y):\n xip:=xi-pas*X/NN; yip :=yi+pas*Y/NN;\n X1:=By(xip,yip): Y1:=Bx(xip,yip):NN1:=normE( X1,Y1):\n xi:=xi-pas*(X/NN+X1/NN1)/2;\n yi:=yi+pas*( Y/NN+Y1/NN1)/2;\n liste:=[-xi,yi],liste,[xi,yi]:\n t tamp:=theta(xi,yi):\n delta:=min(abs(ttamp-ti),abs(pi-abs(tta mp-ti))) :\n t:=t+delta:\n if delta<0.01 then pas:= 2*pas \n elif delta>0.04 then pas:=pas/2 fi;\n ti :=ttamp:\n od;\n evalf([liste]):\nend:" }}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 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