1
$\begingroup$

in the beginning of the code I have:

 θ[t_] := Array[Subscript[θ, #][t] &, n];

Then after defining the differential equations and the constrains in EQ I can solve them and Plot them like this:

 s = NDSolve[EQ, θ[t], {t, 0, 100}, Method -> {"EquationSimplification" -> "Residual"} ]

 Plot[Evaluate[θ[t] /. s], {t, 0, 10}, PlotRange -> All, PlotLegends -> Automatic]

But when I try a ParametricPlot, it no longer works:

 ParametricPlot[Evaluate[{θ[t] /. s, θ'[t] /. s]}, {t, 0, 10}, PlotRange -> All, PlotLegends -> Automatic]

Any idea why? (I think it is in the θ'[t], but I dont know why)

EDIT (all code)

n = 2;
g = 9.8;
m = {};
l = {};
EOM = Array[# &, n];

For[i = 1, i <= n, ++i,
   AppendTo[m, 0.1];
   AppendTo[l, 0.5];]

\[Theta][t_] := Array[Subscript[\[Theta], #][t] &, n];

Ec[t_] := 0.5*Sum[(n + 1 - i)*m[[i]]*(l[[i]]^2* (Subscript[\[Theta], i]'[t])^2 + Sum[2*l[[i]]*l[[k]]*Subscript[\[Theta], i]'[t] *Subscript[\[Theta], k]'[t] * Cos[Subscript[\[Theta], k][t] - Subscript[\[Theta], i][t]], {k, 1, i - 1}]), {i, 1, n}];

Ep[t_] := -g*Sum[  (n + 1 - i)*m[[i]]*l[[i]]*Cos[Subscript[\[Theta], i][t]]   , {i, 1, n}];

Lagrangiano[t_] = Ec[t] - Ep[t];

For[i = 1, i <= n, ++i,
EOM[[i]] = 
    D[D[Lagrangiano[t], Subscript[\[Theta], i]'[t]], t] - 
    D[Lagrangiano[t], Subscript[\[Theta], i][t]] == 0]


thetainicial = Array[# &, n];
Dthetainicial = Array[# &, n];
For[i = 1, i <= n, ++i,
   thetainicial[[i]] = Subscript[\[Theta], i][0] == Pi/4;
   Dthetainicial[[i]] = Subscript[\[Theta], i]'[0] == 0]
EQ = Join[EOM, thetainicial, Dthetainicial];

s = NDSolve[EQ, \[Theta][t], {t, 0, 100}, Method -> {"EquationSimplification" -> "Residual"} ]

Plot[Evaluate[\[Theta][t] /. s], {t, 0, 10}, PlotRange -> All, PlotLegends -> Automatic]

Everything fine until this:

Plot[Evaluate[\[Theta]'[t] /. s], {t, 0, 10}, PlotRange -> All, PlotLegends -> Automatic]

ParametricPlot[Evaluate[{\[Theta][t] /. s, \[Theta]'[t] /. s}], {t, 0, 10}, PlotRange -> All, PlotLegends -> Automatic]

Neither one works.

$\endgroup$
  • $\begingroup$ New EDIT. Thanks $\endgroup$ – ines Jun 23 '17 at 15:35
  • $\begingroup$ Try s = Flatten@NDSolve[EQ, {θ[t], θ'[t]}, {t, 0, 100}, ... $\endgroup$ – bbgodfrey Jun 23 '17 at 15:42
  • $\begingroup$ Doesn't change anything. The problem seems to by that θ'[t] equals zero always, but this shouldn't be happening $\endgroup$ – ines Jun 23 '17 at 15:49
  • $\begingroup$ Without an expression for Lagrangiano, it is difficult to provide additional advice. $\endgroup$ – bbgodfrey Jun 23 '17 at 15:51
  • $\begingroup$ Ec[t_] := 0.5*Sum[(n + 1 - i)*m[[i]]*(l[[i]]^2* (Subscript[[Theta], i]'[t])^2 + Sum[2*l[[i]]*l[[k]]*Subscript[[Theta], i]'[t] Subscript[[Theta], k]'[t] * Cos[Subscript[[Theta], k][t] - Subscript[[Theta], i][t]], {k, 1, i - 1}]), {i, 1, n}]; Ep[t_] := -gSum[ (n + 1 - i)*m[[i]]*l[[i]]*Cos[Subscript[[Theta], i][t]] , {i, 1, n}]; Lagrangiano[t_] = Ec[t] - Ep[t]; $\endgroup$ – ines Jun 23 '17 at 15:55
1
$\begingroup$

The following modifications provide what I think is the desired answer.

s = Flatten@NDSolve[EQ, θ[t], {t, 0, 100}, 
    Method -> {"EquationSimplification" -> "Residual"}];

to eliminate an extra {}. Then, as before, θ[t] is obtained by

Plot[Evaluate[θ[t] /. s], {t, 0, 10}, PlotLegends -> Automatic]

enter image description here

The other two plots require modified code:

Plot[Evaluate[D[θ[t] /. s, t]], {t, 0, 10}, PlotLegends -> Automatic] 
ParametricPlot[Evaluate[Transpose@{θ[t] /. s, D[θ[t] /. s, t]}], {t, 0, 10}, 
    AspectRatio -> 1, PlotLegends -> Automatic]

enter image description here

enter image description here

Transpose is needed to pair each θ'[t] with the corresponding θ[t],

$\endgroup$
  • $\begingroup$ YES!!!! Thank you! $\endgroup$ – ines Jun 23 '17 at 16:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for?Browse other questions tagged or ask your own question.