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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115168] NDSolve, three 2-d order ODE, 6 initial conditions
  • From: michael partensky <partensky at gmail.com>
  • Date: Mon, 3 Jan 2011 03:56:52 -0500 (EST)

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



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