{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 "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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 549 "addi:=proc(A,B,a,b) \n [seq(A[i]*a+B[i]*b,i=1..3)]\n end:\n scal:=proc(A,B)\n add(A[i]*B[i ],i=1..3)\n end:\n M:=[x(t),cos(u(t)),sin(u(t))]:\n dM:=diff(M,t):ds:= sqrt(simplify(scal(dM,dM))):\nU:=addi(dM,0,(sin(u(t))-z0)/ds,0):U:=dif f(U,t):\nU:=simplify(addi(U,[0,0,-ds],ds^3,ds^3)):\n V:=[0,cos(u(t)), \+ sin(u(t))]:\n A:=simplify((U[2]*V[3]-U[3]*V[2])/diff(x(t),t)):\nsols:= solve(\{A,diff(x(t),t)^2*cos(u(t))+diff(u(t),t)^2*cos(u(t))-sin(u(t))* diff(u(t),`$`(t,2))\},\{diff(u(t),t,t),diff(x(t),t,t)\}):\nsols:=solve (\{A,diff(x(t),t,t)=0\},\{diff(u(t),t,t),diff(x(t),t,t)\}):\n " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 207 "equa:=\{op(subs(z0=-2.2,sol s)),u(0)=Pi/2,x(0)=0,D(u)(0)=-1,D(x)(0)=-1\}:\n\n solu:=dsolve(equa,\{ u(t),x(t)\},numeric,method=rkf45,output=listprocedure):\n uu:=subs(sol u,u(t)):\n xx:=subs(solu,x(t)):\n inter:=0..5.3:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 190 "equa:=\{op(subs(z0=0,sols)),u(0)=Pi/2,x(0)= 0,D(u)(0)=-1,D(x)(0)=-1\}:\n\n solu:=dsolve(equa,\{u(t),x(t)\},numeric ,method=rkf45,output=listprocedure):\n uu2:=subs(solu,u(t)):\n xx2:=s ubs(solu,x(t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 393 "cyl:=pl ot3d([tt,cos(t),sin(t)],tt=xx(op(1,inter))..xx(op(2,inter)),t=0..2*Pi, grid=[2,100]):\ndisplay(spacecurve(\{[xx(t),1.02*cos(uu(t)),1.02*sin(u u(t))],[xx2(t),1.02*cos(uu2(t)),1.02*sin(uu2(t))]\},t=inter,thickness= 3,color=red,numpoints=50),spacecurve(\{\n[xx(t),0,1,t=inter]\},thickne ss=2,color=blue,numpoints=50),cyl,style=patchnogrid,scaling=constraine d,lightmodel=light2,orientation=[106,45]);" }}{PARA 13 "" 1 "" {GLPLOT3D 496 496 496 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