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MathGroup Archive 2006

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Re: How to plot field lines ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72208] Re: How to plot field lines ?
  • From: "Narasimham" <mathma18 at hotmail.com>
  • Date: Thu, 14 Dec 2006 05:49:33 -0500 (EST)
  • References: <elos9v$oiq$1@smc.vnet.net>

Cham wrote:
> Hello,  I'm new here.
>
> I have some complicated deformed dipolar magnetic field in cartesian components, and I need to show
> some field lines.  I'll also have to extract coordinates of lines to a list.  How should I do that ?

> I can use the code below (with properly defined functions fx, fy and fz), but it's unreliable
> (it frequently hit the singularity at the center) and it frequently gives many unpredictable curves.
> Any idea ?  Please, I need help !  :-(
>
> FieldCurve = NDSolve[{
>
> x'[t] == fx[ x[t], y[t], z[t] ], y'[t] == fy[ x[t], y[t], z[t] ], z'[t] == fz[ x[t], y[t], z[t] ],
>
> x[0] == ... number ...,
> y[0] == ... number ...,
> z[0] == ... number ...
>
> }, {x, y, z}, {t, 0, 100}, MaxSteps -> 10000]
>
> Graph = ParametricPlot3D[
> 		Evaluate[{x[t], y[t], z[t]}/. FieldCurve],
> 		{t, 0, 100}, PlotPoints -> 1000]
------
" It works fine for some right hand side  functions/BC chosen as above.
Check how your functions behave at required critical points by
beginning with simple functions. Avoid giving BC at or near
singularities, i.e.,near positive/negative charges/source/sinks &c."
<< RealTime3D`
tm = 50 ;
FieldCurve = NDSolve[{
x'[t] == Sin[ z[t]] - y[t],
y'[t] == x[t] - Cos[z[t]],
z'[t] == -Sin[y[t]] + x[t] ,
x[0] == 2, y[0] == 1, z[0] == 0 }, {x, y, z}, {t, 0, tm}, MaxSteps ->
10000] ;
Graph = ParametricPlot3D[ Evaluate[{x[t], y[t], z[t]} /. FieldCurve],
{t, 0,tm}, PlotPoints -> 1000] ;

Narasimham


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