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Re: NDSolve, three 2-d order ODE, 6 initial conditions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg115246] Re: NDSolve, three 2-d order ODE, 6 initial conditions
*From*: michael partensky <partensky at gmail.com>
*Date*: Tue, 4 Jan 2011 18:52:50 -0500 (EST)
Thanks Robert, and everybody.
The issue is resolved.
Although there was indeed a typo in the third equation,
I used the correct system (sorry for not updating the post).
Turned out that it was a bug in 7.0 (and also a bug in 7.01 producing a
different error message ) , that have been fixed in 8.0.
The details are described in my response to DrMajorBob
Thanks for all your help and great advises.
Now I have another problem, with the parametric plot in M. 8, but this
deserves a special discussion thread.
Basically, my several attempts to rescale and reorient the plot resulted in
severe errors and rebooting the computer (windows XP). I will try some
ideas implemented in Robert's solution - may be they will help.
Best
MP
On Tue, Jan 4, 2011 at 8:32 AM, Dr. Robert Kragler <kragler at hs-weingarten.de
> wrote:
> Anbei ein Mma-Notebook (V5.2) mit der L=F6sung.
> Gru=DF R. Kragler
>
>
> Am 03.01.2011 09:56, schrieb michael partensky:
>
> Hi, group!
>
> An attempt to demonstrate a (restricted) analogy between the Bloch
> (magnetic resonance) equation and the motion equation for a charged particle
> in the magnetic field leads to the following equation:
>
> 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}];
>
> Apparently there is an error - u will see the message. Could you please help
> catching it?
> Thanks
> Michael Partenskii
>
>
>
>
>
> --
> Prof. Dr. Robert Kragler
> Hasenweg 5
> D-88090 Immenstaad, Germany
> Phone : +49 (7545) 2833 or 3500
> Email : kragler at hs-weingarten.de
> URL : http://www.hs-weingarten.de/~kragler
>
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