In[584]:= Subscript[B, v] = D[L, x'[t], t] - D[L, x[t]]
Out[584]=
1. Subscript[\[Rho],
Wasser] \[CurlyPhi][t] Derivative[1][x][t] Derivative[
1][\[CurlyPhi]][t] +
1. M (x^\[Prime]\[Prime])[
t] - (-0.3 - 0.3 Subscript[\[Alpha], FlosseHinten] +
0.3 Subscript[\[Alpha], FlosseVorne]) Subscript[\[Rho],
Wasser] (x^\[Prime]\[Prime])[t] +
0.5 Subscript[\[Rho],
Wasser] \[CurlyPhi][t]^2 (x^\[Prime]\[Prime])[t] +
2 bv Derivative[1][x][t] (x^\[Prime]\[Prime])[t] + (
4 M \[Pi] Subscript[l, Masse] (\[Phi]^\[Prime]\[Prime])[t])/
Derivative[1][\[Phi]][t]^2
In[585]:= Subscript[B, quer] = D[L, y'[t], t] - D[L, y[t]]
Out[585]=
1. M (y^\[Prime]\[Prime])[t] +
2 Subscript[b, quer] Derivative[1][y][t] (y^\[Prime]\[Prime])[t]
In[586]:= Subscript[B, beta] = D[L, \[Beta]'[t], t] - D[L, \[Beta][t]]
Out[586]= -Subscript[b, beta] \[Beta][t]^2 -
0.000565056 E^(-0.28 Sqrt[\[Beta][t]^2]) M \[Beta][t]^5 + (
0.0000263693 E^(-0.28 Sqrt[\[Beta][t]^2])
M \[Beta][t]^7)/Sqrt[\[Beta][t]^2] +
1. Subscript[J, \[Beta]] (\[Beta]^\[Prime]\[Prime])[t]
In[587]:= Subscript[B, phi ] =
D[L, \[CurlyPhi]'[t], t] - D[L, \[CurlyPhi][t]]
Out[587]= -Subscript[b, phi] \[CurlyPhi][t]^2 +
0.0753408 E^(-0.23 Sqrt[\[CurlyPhi][t]^2]) M \[CurlyPhi][t]^3 - (
0.0043321 E^(-0.23 Sqrt[\[CurlyPhi][t]^2])
M \[CurlyPhi][t]^5)/Sqrt[\[CurlyPhi][t]^2] -
0.5 Subscript[\[Rho], Wasser] \[CurlyPhi][t] Derivative[1][x][t]^2 +
1. Subscript[J, \[CurlyPhi]] (\[CurlyPhi]^\[Prime]\[Prime])[t]
In[588]:= Subscript[B, omega ] = D[L, \[Phi]'[t], t] - D[L, \[Phi][t]]
Out[588]= -Subscript[b, omega] \[Phi][t]^2 + (
4 M \[Pi] Subscript[l, Masse] (x^\[Prime]\[Prime])[t])/
Derivative[1][\[Phi]][t]^2 +
1. Subscript[J, \[Phi]] (\[Phi]^\[Prime]\[Prime])[t] - (
8 M \[Pi] Subscript[l, Masse]
Derivative[1][x][t] (\[Phi]^\[Prime]\[Prime])[t])/
Derivative[1][\[Phi]][t]^3
In[589]:=
In[590]:=
In[595]:= DSolve[{Subscript[B, v] == 0, Subscript[B, quer] == 0,
Subscript[B, phi ] == 0, Subscript[B, beta] == 0,
Subscript[B, omega ] == 0, x[0] == 0 ,
x'[0] == Subscript[c, vv], y[0] == 0 ,
y'[0] == Subscript[c, vquer], \[Beta][0] == Subscript[c,
sbeta], \[Beta]'[0] == Subscript[c,
vbeta ], \[CurlyPhi][0] == Subscript[c,
sphi] , \[CurlyPhi]'[0] == Subscript[c, vphi], \[Phi][0] ==
Subscript[c, somega], \[Phi]'[0] == Subscript[c,
vomega]} , {x[t],
y[t], \[CurlyPhi][t], \[Beta][t], \[Phi][t]} , t]
During evaluation of In[595]:= DSolve::dvnoarg: The function \[CurlyPhi] appears with no arguments.
Out[595]= DSolve[{1. Subscript[\[Rho],
Wasser] \[CurlyPhi][t] Derivative[1][x][t] Derivative[
1][\[CurlyPhi]][t] +
1. M (x^\[Prime]\[Prime])[
t] - (-0.3 - 0.3 Subscript[\[Alpha], FlosseHinten] +
0.3 Subscript[\[Alpha], FlosseVorne]) Subscript[\[Rho],
Wasser] (x^\[Prime]\[Prime])[t] +
0.5 Subscript[\[Rho],
Wasser] \[CurlyPhi][t]^2 (x^\[Prime]\[Prime])[t] +
2 bv Derivative[1][x][t] (x^\[Prime]\[Prime])[t] + (
4 M \[Pi] Subscript[l, Masse] (\[Phi]^\[Prime]\[Prime])[t])/
Derivative[1][\[Phi]][t]^2 == 0,
1. M (y^\[Prime]\[Prime])[t] +
2 Subscript[b, quer]
Derivative[1][y][t] (y^\[Prime]\[Prime])[t] ==
0, -Subscript[b, phi] \[CurlyPhi][t]^2 +
0.0753408 E^(-0.23 Sqrt[\[CurlyPhi][t]^2]) M \[CurlyPhi][t]^3 - (
0.0043321 E^(-0.23 Sqrt[\[CurlyPhi][t]^2]) M \[CurlyPhi][t]^5)/
Sqrt[\[CurlyPhi][t]^2] -
0.5 Subscript[\[Rho],
Wasser] \[CurlyPhi][t] Derivative[1][x][t]^2 +
1. Subscript[J, \[CurlyPhi]] (\[CurlyPhi]^\[Prime]\[Prime])[t] ==
0, -Subscript[b, beta] \[Beta][t]^2 -
0.000565056 E^(-0.28 Sqrt[\[Beta][t]^2]) M \[Beta][t]^5 + (
0.0000263693 E^(-0.28 Sqrt[\[Beta][t]^2]) M \[Beta][t]^7)/
Sqrt[\[Beta][t]^2] +
1. Subscript[J, \[Beta]] (\[Beta]^\[Prime]\[Prime])[t] ==
0, -Subscript[b, omega] \[Phi][t]^2 + (
4 M \[Pi] Subscript[l, Masse] (x^\[Prime]\[Prime])[t])/
Derivative[1][\[Phi]][t]^2 +
1. Subscript[J, \[Phi]] (\[Phi]^\[Prime]\[Prime])[t] - (
8 M \[Pi] Subscript[l, Masse]
Derivative[1][x][t] (\[Phi]^\[Prime]\[Prime])[t])/
Derivative[1][\[Phi]][t]^3 == 0, x[0] == 0,
Derivative[1][x][0] == Subscript[c, vv], y[0] == 0,
Derivative[1][y][0] == Subscript[c, vquer], \[Beta][0] == Subscript[
c, sbeta],
Derivative[1][\[Beta]][0] == Subscript[c, vbeta], \[CurlyPhi][0] ==
Subscript[c, sphi],
Derivative[1][\[CurlyPhi]][0] == Subscript[c, vphi], \[Phi][0] ==
Subscript[c, somega],
Derivative[1][\[Phi]][0] == Subscript[c, vomega]}, {x[t],
y[t], \[CurlyPhi][t], \[Beta][t], \[Phi][t]}, t]