I want to programm a N-Pendulum(the Idea comes from the Doublependulum). And i have the following Problem:
v[q_]:=Sum[Subscript[l, n]Sin[Subscript[\[Phi], n][t]],{n,1,q,1}]
w[q_]:=Sum[-Subscript[l, n]Cos[Subscript[\[Phi], n][t]],{n,1,q,1}]
vko=Subscript[l, 1]Sin[Subscript[\[Phi], 1][t]]
wko=-Subscript[l, 1]Cos[Subscript[\[Phi], 1][t]]
These are the Koordinates of for the mass of the first pendulum. But what happens now is more a technical problem of mathematica, i think.
I put the first point (v,w) in to the kinetic energy:
Tkin = Sum[
Subscript[m, q]/2 (D[v[q], t]^2 + D[w[q], t]^2), {q, 1, 1, 1}]
Out:
1/2 Subscript[m, 1] (Cos[Subscript[\[Phi], 1][t]]^2
\!\(\*SubsuperscriptBox[\(l\), \(1\), \(2\)]\) Derivative[1][
Subscript[\[Phi], 1]][t]^2 + Sin[Subscript[\[Phi], 1][t]]^2
\!\(\*SubsuperscriptBox[\(l\), \(1\), \(2\)]\) TextCell[
""]^2 Derivative[1][Subscript[\[Phi], 1]][t]^2)
The Second Point (vko,wko)
Tkin = Sum[
Subscript[m, q]/2 (D[vko, t]^2 + D[wko, t]^2), {q, 1, 1, 1}]
Out:
1/2 Subscript[m, 1] (Cos[Subscript[\[Phi], 1][t]]^2
\!\(\*SubsuperscriptBox[\(l\), \(1\), \(2\)]\) Derivative[1][
Subscript[\[Phi], 1]][t]^2 + Sin[Subscript[\[Phi], 1][t]]^2
\!\(\*SubsuperscriptBox[\(l\), \(1\), \(2\)]\) Derivative[1][
Subscript[\[Phi], 1]][t]^2)
In the first Out u see: mathematica put " ^2" in the solution. But when i give mathematica the koord without the sum, it gives the correct solution without the Textcell[""]^2.
How can i bring mathematica to stop generating this Textcell?
