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Manipulate in a ParametricPlot

Alexandra Man
Posted 5 years ago

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}]
POSTED BY: Alexandra Man
6 Replies
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Move the definitions of t21, t31, t23, t33 inside the Manipulate, otherwise they will not get updated:

Manipulate[t21 = (2*Pi/lambda[[1]])*l22; t31 = (2*Pi/lambda[[1]])*l33;
  t23 = (2*Pi/lambda[[5]])*l22;
 t33 = (2*Pi/lambda[[5]])*l33; 
 Plot[{2*Y1*Tan[t11] + Y2*Tan[t21] + Y9*Tan[t31], 
   2*Y1*Tan[t13] + Y2*Tan[t23] + Y9*Tan[t33], 
   t11*Y1 + t21*(Y2/2)*(Sec[t21]^2/Sec[t11]^2) + 
    t31*(Y9/2)*(Sec[t31]^2/Sec[t11]^2) - b1, 
   t13*Y1 + t23*(Y2/2)*(Sec[t23]^2/Sec[t13]^2) + 
    t33*(Y9/2)*(Sec[t33]^2/Sec[t13]^2) - b3},
  {Y2, 0.008, 0.05}],
 {Y9, 0.008, 0.05}, {l33, 0.008, 0.012}, {l22, 0.008, 0.012}]
POSTED BY: Gianluca Gorni
Updating Name
Updating Name
Posted 4 years ago

Thanks a lot. It worked perfectly.
POSTED BY: Updating Name
Alexandra Man
Alexandra Man
Posted 5 years ago
POSTED BY: Alexandra Man

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.
POSTED BY: Hans Dolhaine

Hi. I would like to plot four equations with four variables by using the manipulate function. But the code was not able to plot the four equations. Can you please check the syntax and tell me what's wrong?

Y2=.;Y9=.;l22=.;l33=.;Y1=0.02;l1=0.0105698;lambda={0.0426,0.0401,0.0403,0.0423,0.0413};b1=0.0804031;b3=0.0258706;
    t21=(2*Pi/lambda[[1]])*l22;t31=(2*Pi/lambda[[1]])*l33;t23=(2*Pi/lambda[[5]])*l22;
    t33=(2*Pi/lambda[[5]])*l33;t11=(2*Pi/lambda[[1]])*l1;t13=(2*Pi/lambda[[5]])*l1;
  Manipulate[Plot[{2*Y1*Tan[t11]+Y2*Tan[t21]+Y9*Tan[t31],
      2*Y1*Tan[t13]+Y2*Tan[t23]+Y9*Tan[t33],
      t11*Y1+t21*(Y2/2)*(Sec[t21]^2/Sec[t11]^2)+t31*(Y9/2)*(Sec[t31]^2/Sec[t11]^2)-b1,
      t13*Y1+t23*(Y2/2)*(Sec[t23]^2/Sec[t13]^2)+t33*(Y9/2)*(Sec[t33]^2/Sec[t13]^2)-b3},
     {Y2,0.008,0.05}],{Y9,0.008,0.05},{l33,0.008,0.012},{l22,0.008,0.012}]
POSTED BY: Sunanda Lakkimsetti

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
POSTED BY: Hans Dolhaine
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