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Avoid error with DSolve (functions appear with no arguments)?

Posted 5 months ago
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Hello =)

I dont understand the DSolve Error i got on this differntial equations system. Some ideas? Thanks!

enter image description here

POSTED BY: ha bla
Answer
4 Replies

post your code using the code sample icon (the first one)

Posted 5 months ago

Posted

POSTED BY: ha bla
Answer
Posted 5 months ago
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]
POSTED BY: ha bla
Answer

Beware that (x^\[Prime]\[Prime])[t] is not the same as x''[t], even though when typeset they look exactly alike. To enter the derivative sign use the apostrophe, as in the good old ascii days. You also use \[CurlyPhi] as a subscript, which may be the cause of the error message.

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