{VERSION 5 0 "IBM INTEL LINUX" "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 "" 0 1 0 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 Output" 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" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 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 0 823 "restart:\na:=1;\nU: =1;\n#A:=10;\nA:=0.3;\nPhi:=A*theta + U*(r+a^2/r)*cos(theta);\nx:=r*co s(theta): y:=r*sin(theta):\nplot3d([x,y,Phi],r=a..4*a,theta=0..2*Pi,ax es=boxed,style=patchcontour);\nplots[contourplot]([x,y,Phi],r=a..4*a,t heta=0..2*Pi,axes=boxed,filled=true);\ner:=[cos(theta),sin(theta)]:\ne t:=[-sin(theta),cos(theta)]:\nV:=expand(diff(Phi,r)*er+et*diff(Phi,the ta)/r);\nr2V:=expand(V*r^2);\nlenV:=sqrt(V[1]^2+V[2]^2):\nnr:=10:\nnt: =50:\nrmin:=a:\nrmax:=4*a:\nvscale:=0.25;\nfor i from 0 to nr do\n r :=rmin+i*(rmax-rmin)/nr;\n for j from 0 to nt do\n theta:=j*2*P i/nt;\n#print(r,theta,x,y);\n arr[i,j]:=\n plottools[line ]([x-vscale*V[1],y-vscale*V[2]],[x+vscale*V[1],y+vscale*V[2]] );\n \+ od: unassign('j','theta'):\nod: unassign('i','r'):\n#plots[display](se q( seq(arr[i,j],j=0..nt),i=0..nr ),style=patchcontour); " }} {PARA 13 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"a G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG\"\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"AG$\"\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PhiG,&*&$\"\"$!\"\"\"\"\"%&thetaGF*F**&,&%\"rGF**&F*F*F.F)F*F *-%$cosG6#F+F*F*" }}{PARA 13 "" 1 "" {GLPLOT3D 289 289 289 {PLOTDATA 3 "6%-%%MESHG6#X.%)anythingG6\"6\"[gl'!%\"!!$^`r\":\":\"$3FF0000000000 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"6#>%'vscaleG$\"#D!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1212 "restart:\na:=1;\nU:=1;\nA:=0.0;\nVcart:=proc(x,y)\n local r:\n r:=sqrt(x^2+y^2);\n [(1/r^2)*(-A*y+U*y^2+U*a^2*y^ 2/r^2 + U*x^2 -U*a^2*x^2/r^2),\n (1/r^2)*(A*x -2*U *a^2*x*y/r^2)];\nend:\nVcart(0,1);\nnx:=30;\nny:=30;\nxmin:=-3*a;\nxma x:=3*a;\nymin:=-3*a;\nymax:=3*a;\n\nsp:=plots[contourplot](sqrt(Vcart( x,y)[1]^2+Vcart(x,y)[2]^2),x=xmin..xmax,y=ymin..ymax,\n levels= [seq(.2*k,k=1..10)],filled=true,grid=[80,80],scaling=constrained):\ndp :=plottools[disk]([0,0],a,color=white):\nplots[display](dp,sp); \nVcar t:=proc(x,y)\n local r:\n r:=sqrt(x^2+y^2);\n if r^2>a^2 then [(1/r^2)*(-A*y+U*y^2+U*a^2*y^2/r^2 + U*x^2 -U*a^2*x^2/r^2),\n \+ (1/r^2)*(A*x -2*U*a^2*x*y/r^2)];\n else\n [0,0]; \n fi:\nend:\nvscale:=0.15;\nfor i from 0 to nx do\n x:=xmin+i*(x max-xmin)/nx;\n#print(x);\n for j from 0 to ny do\n y:=ymin+j*( ymax-ymin)/ny;\n p1:=evalf([x-vscale*Vcart(x,y)[1],y-vscale*Vcart (x,y)[2]]);\n p2:=evalf([x+vscale*Vcart(x,y)[1],y+vscale*Vcart(x, y)[2]]);\n#print(p1);\n arr[i,j]:=\n plottools[line](p1,p 2);\n od: unassign('j','y'):\nod: unassign('i','x'):\nplots[display] (seq( seq(arr[i,j],j=0..ny),i=0..nx ),scaling=constrained,\ntitle=\"sp eed field\"); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\" \"#\"\"!$F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nxG\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nyG\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%%xminG!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xmaxG\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%yminG!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ymaxG\"\"$" }}{PARA 13 "" 1 "" {GLPLOT2D 585 496 496 {PLOTDATA 2 "6;-%)POLYGONSG6$7U7$$\"\"\"\"\"!$F*F*7$$\"+8q9@**!#5$ \"+OBL`7F/7$$\"+6;$eo*F/$\"+t))*o[#F/7$$\"+f[w(H*F/$\"+FbC\"o$F/7$$\"+ 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