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 don't 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}]