# Manipulate in a ParametricPlot

Posted 3 months ago
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 Hello, I used ParamtericPlot for obtaining curves by Euler elasticity theory. The shape of the curve depends on alpha variable which is initial angle in this issue. I am trying to use Manipulate in a ParametricPlot and changing alpha but something is wrong (the shape of the curve is constant, but I dont know how to plot it without prior defining alpha). I would really appreciate your help and advise. Regards  l = 300; \[Alpha] = 130 Degree; k = Sin[\[Alpha]/2]^2; m = 2; \[Lambda]L = (2*m*EllipticK[k])/l; x1L[s_] := -s + 2/\[Lambda]L (EllipticE[ JacobiAmplitude[s*\[Lambda]L + EllipticK[k], k], k] - EllipticE[JacobiAmplitude[EllipticK[k], k], k]); x2L[s_] := -2 k/\[Lambda]L (JacobiCN[EllipticK[k] + (s*\[Lambda]L), k]); Manipulate[ ParametricPlot[{x1L[s], x2L[s]}, {s, 0, l}, AxesLabel -> {x, y}, LabelStyle -> {FontSize -> 10, Darker[Black], Bold}, PlotLegends -> "xlocal"], {\[Alpha], 0, 2 Pi}] 
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Posted 3 months ago
 Try this, but it seems that there is some difficulty at alpha = Pi: Complex Infinity encountered. l = 300; k[\[Alpha]_] := Sin[\[Alpha]/2]^2; m = 2; \[Lambda]L = (2*m*EllipticK[k[\[Alpha]]])/l; x1L[s_] := -s + 2/\[Lambda]L (EllipticE[ JacobiAmplitude[s*\[Lambda]L + EllipticK[k[\[Alpha]]], k[\[Alpha]]], k[\[Alpha]]] - EllipticE[JacobiAmplitude[EllipticK[k[\[Alpha]]], k[\[Alpha]]], k[\[Alpha]]]); x2L[s__] := -2 k[\[Alpha]]/\[Lambda]L (JacobiCN[ EllipticK[k[\[Alpha]]] + (s*\[Lambda]L), k[\[Alpha]]]); Manipulate[ ParametricPlot[{x1L[s], x2L[s]} /. \[Alpha] -> aa, {s, 0, l}, AxesLabel -> {x, y}, LabelStyle -> {FontSize -> 10, Darker[Black], Bold}, PlotRange -> {-60, 60}], {{aa, Pi/2}, 0, 2 Pi}] x1L[.2] /. \[Alpha] -> Pi x2L[.2] /. \[Alpha] -> Pi 
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Posted 3 months ago
 Thank you for your response. In fact, using this code, the boundary condition is changed (the right end of the curve should move along the horizontal axis). However, it is very helpful for me, I will study this code and try to adapt it to my needs.
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Posted 3 months ago
 Hi Alexandra,change the PlotRange to {{-300, 300}, {-100, 100}} , then you see that the right end of the curves moves along the horizontal axis from right to left, the left end stays at the origin.
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