{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "" 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 " restart;\n e1 := ( X(t)-x)^2+(Y(t)-y)^2=S^2;\n e2 := F(x,y)=0;\n #position := fsolve(\{su bs(t=1.2,e1),e2\},\{x,y\},\n # \{x=x1..x2,y=y1..y2\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 " xyt := [x=x(t),y=y(t)]:\n e 1 := subs(xyt,e1);\n e2 := subs(xyt,e2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 209 " Su0 := [DX=X-x,DY=Y-y]:\n Su1 := [diff(X(t),t)=Xt,d iff(Y(t),t)=Yt,\n diff(x(t),t)=xt,diff(y(t),t)=yt,\n D [1](F)(x(t),y(t))=Fx(x,y),D[2](F)(x(t),y(t))=Fy(x,y),\n X(t)=D X+x(t),Y(t)=DY+y(t)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " e 1d := subs(Su1,diff(e1,t));\n e2d := subs(Su1,diff(e2,t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 " Velocity := subs(subs(Su0,solve(\{ e1d,e2d\},\{xt,yt\})),[xt,yt]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 283 " Su0t := [DXt=Xt-xt,DYt=Yt-yt]:\n Su2 := [diff(X(t),t,t)=Xtt, diff(Y(t),t,t)=Ytt,\n diff(x(t),t,t)=xtt, diff(y(t),t,t)=ytt] ;\n Su3 := [Xt=DXt+xt, Yt=DYt+yt]:\n Su4 := [D[1,1](F)(x(t),y(t))=Fxx( x,y),\n D[2,2](F)(x(t),y(t))=Fyy(x,y),\n D[1,2](F)(x(t ),y(t))=Fxy(x,y)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 " e1dd := subs(Su2,Su1,Su3,diff(e1,t,t));\n e2dd := subs(Su2,Su1,Su4,diff(e2 ,t,t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 " acceleration : = solve(\{e1dd,e2dd\},\{xtt,ytt\}):\n Acceleration := subs(subs(Su0t,S u0,\n collect(acceleration,[DX,DY,Fx,Fy])),[xtt,ytt]): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 246 " Vx := unapply(Velocit y[1],X,Y,Xt,Yt,x,y);\n Vy := unapply(Velocity[2],X,Y,Xt,Yt,x,y);\n Ax \+ := unapply(Acceleration[1],X,Y,Xt,Yt,Xtt,Ytt,x,y,xt,yt);\n Ay := unapp ly(Acceleration[2],X,Y,Xt,Yt,Xtt,Ytt,x,y,xt,yt);\n save Vx, Vy, Ax, Ay , \"Functions.sav\":" }}}{EXCHG }}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }