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Re: NDSolve, three 2-d order ODE, 6 initial conditions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115239] Re: NDSolve, three 2-d order ODE, 6 initial conditions
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Tue, 4 Jan 2011 18:51:31 -0500 (EST)

You're saying, I think, that the following relationship reduces the  
differential order of the system to 5??

Solve[0 ==
   2 (Sin[5 t] Derivative[1][x][t] - Cos[2 t] Derivative[1][y][t]),
  y'[t]]

{{Derivative[1][y][t] -> Sec[2 t] Sin[5 t] Derivative[1][x][t]}}

Bobby

On Tue, 04 Jan 2011 03:29:22 -0600, Alois Steindl  
<Alois.Steindl at tuwien.ac.at> wrote:

> Am 03.01.2011 09:56, schrieb michael partensky:
>> ndSol[w_, w0_, w1_, x0_, y0_, z0_, v0x_, v0y_, v0z_, t1_] :=
>>    NDSolve[{Cos[w t ] D[x[t], {t, 2}] + Sin[ w t] D[y[t], {t, 2}] - w  
>> Sin[w
>> t] D[x[t], t] + w Cos[w t] D[y[t], t] == (w - w0) ( Sin[w t ] D[x[t],  
>> t] -
>> Cos[w t] D[y[t], t]),
>>      -Sin[w t] D[x[t], {t, 2}] + Cos[w t] D[y[t], {t, 2}] == (w - w0)  
>> (Cos[w
>> t] D[x[t], t] + Sin[w t] D[y[t], t]) + w1 D[z[t], t],
>>      D[z, {t, 2}] == w1 (Sin[w t] D[x[t], t] - Cos[w1 t] D[y[t], t]),
>> (D[x[t], t] /. {t ->  0} ) == v0x, (D[y[t], t] /. {t ->  0} ) == v0y,  
>> (D[z[t],
>> t] /. {t ->  0})  == v0z, x[0] == x0, y[0] == y0, z[0] == z0 }, {x[t],  
>> y[t],
>> z[t]}, {t, t1}];
>>
> Hello,
> when I type
> ndSol[5, 3, 2, 0, 0, 0, 0, 0, 0, 10]
> I get the message
> NDSolve::ndnco: The number of constraints (6) (initial conditions) is
> not equal to the total differential order of the system (5). >>
> and the output (converted here to InputForm for better readability):
> NDSolve[{-5*Sin[5*t]*Derivative[1][x][t] +
>           5*Cos[5*t]*Derivative[1][y][t] +
>      Cos[5*t]*Derivative[2][x][t] +
>           Sin[5*t]*Derivative[2][y][t] ==
>         2*(Sin[5*t]*Derivative[1][x][t] -
>        Cos[5*t]*Derivative[1][y][t]),
>       (-Sin[5*t])*Derivative[2][x][t] + Cos[5*t]*Derivative[2][y][t] ==
>         2*(Cos[5*t]*Derivative[1][x][t] +
>         Sin[5*t]*Derivative[1][y][t]) +
>           2*Derivative[1][z][t],
>       0 == 2*(Sin[5*t]*Derivative[1][x][t] -
>              Cos[2*t]*Derivative[1][y][t]), Derivative[1][x][0] == 0,
>       Derivative[1][y][0] == 0, Derivative[1][z][0] == 0, x[0] == 0,
>       y[0] == 0, z[0] == 0}, {x[t], y[t], z[t]}, {t, 10}]
>
> The reason for the message is obvious after looking at the third  
> equation.
> Alois
>


-- 
DrMajorBob at yahoo.com


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