{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 "Warni ng" -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 "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 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 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 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 8 " " 1 "" {TEXT -1 43 "Error, numeric exception: division by zero\n" }} {PARA 7 "" 1 "" {TEXT -1 33 "Warning, computation interrupted\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "a:=1/2:b:=1/3:c:=1/6:d:=2/3 :e:=1/3:C:=4/5:\nx0:=(1+d^2*t^2+2*d*e*t^4+e^2*t^6)/2:\nx:=(a*t+b*t^3+c *t^5)/x0:\ny:=(d*t+e*t^3)/x0:\nz:=-C/x0:t:=tan(tt):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "v1:=diff(x,tt):v2:=diff(y,tt):v3:=diff(z, tt):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "a1:=diff(v1,tt):a2: =diff(v2,tt):a3:=diff(v3,tt):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "b1:=v2*a3-a2*v3:b2:=a1*v3-v1*a3:b3:=v1*a2-a1*v2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "n1:=simplify(v2*b3-b2*v3):n2:=simpl ify(b1*v3-v1*b3):n3:=simplify(v1*b2-b1*v2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dn1:=diff(n1,tt):dn2:=diff(n2,tt):dn3:=diff(n3,tt) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "c1:=n2*dn3-dn2*n3:c2:= dn1*n3-n1*dn3:c3:=n1*dn2-dn1*n2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "facteur:=simplify(sqrt(b1^2+b2^2+b3^2)/(b1*c1+b2*c2+b 3*c3)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "c1:=simplify(c1* facteur):c2:=simplify(c2*facteur):c3:=simplify(c3*facteur):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "rub1:=plot3d([x+u*c1,y+u*c2, z+u*c3],tt=-Pi/2.0001..Pi/2.0001,u=-1/3..1/3,grid=[50,11],style=patch) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "rub2:=plot3d([x+u*c1, y+u*c2,z+u*c3],tt=-Pi/2.0001..Pi/2.0001,u=-1/3..1/3,grid=[300,2],style =patchnogrid):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "normen:= sqrt(n1^2+n2^2+n3^2):n1:=n1/normen:n2:=n2/normen:n3:=n3/normen:\nnorme b:=sqrt(b1^2+b2^2+b3^2):b1:=b1/normeb:b2:=b2/normeb:b3:=b3/normeb:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 198 "rub3:=plot3d([x+u*b1,y+u*b 2,z+u*b3],tt=-Pi/2.001..Pi/2.001,u=0..1/3,grid=[50,2],style=patchnogri d):rub4:=plot3d([x+u*n1,y+u*n2,z+u*n3],tt=-Pi/2.001..Pi/2.001,u=0..1/3 ,grid=[50,2],style=patchnogrid):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "display 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tt):a2:=diff(v2,tt):a3:=diff(v3,tt):\n \+ v1:=diff(x,tt):v2:=diff(y,tt ):v3:=diff(z,tt):\n \+ b1:=v2*a3-a2*v3:b2:=a1*v3-v1*a3:b3:=v1*a2-a1*v2 :\n \+ n1:=simplify(v2*b3-b2*v3):n2:=simplify(b1*v3-v1*b3):n3:=simplif y(v1*b2-b1*v2):\n \+ dn1:=diff(n1,tt):dn2:=diff(n2,tt):dn3:=diff(n3,tt ):\n \+ c1:=n2*dn3-dn2*n3:c2:=dn1*n3-n1*dn3:c3:=n1*dn2-dn1*n2:\n \+ fa cteur:=simplify(sqrt(b1^2+b2^2+b3^2)/(b1*c1+b2*c2+b3*c3)):\n \+ c1:=si mplify(c1*facteur):c2:=simplify(c2*facteur):c3:=simplify(c3*facteur): \n \+ ds:=simplify(sqrt(v1^2+v2^2+v3^2)):\n \+ s:=a->evalf(Int(ds,tt=0 ..a,4))/4:\n \+ d:=a->plot3d([x/s(a)+u*c1/s(a),y/s(a)+u*c2/s(a),(z+2*C )/s(a)+u*c3/s(a)],tt=-a..a,u=-1/3*s(a)..1/3*s(a),grid=[150,2],style=pa tchnogrid):\n \+ n:=40:display([seq(d(k*Pi/2.0001/n,50),k=1..n)],orien tation=[-60,80],lightmodel=light2,insequence=true);" }}{PARA 13 "" 1 " " {GLPLOT3D 526 301 301 {PLOTDATA 3 "6%-%(ANIMATEG6J7#-%%MESHG6$X.%)an ythingG6\"6\"[gl'!%\"!!$_cn\"at\"#\"$C006658AC1EC1D18C00969411EF074F63 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