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Playing with numerically integrated fields?

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  • Subject: [mg97648] Playing with numerically integrated fields?
  • From: Erik Max Francis <max at>
  • Date: Wed, 18 Mar 2009 04:51:00 -0500 (EST)

I'm experimenting with the fields (gravitational, electric, magnetic) of 
extended objects that I'm visualizing through VectorPlot/VectorPlot3D, 
StreamPlot, and ContourPlot and examining the behavior of the motion of 
particles through.  These are all excellent tools, but I have some 
random questions regarding them.  My situation specifically involves the 
situation where I'm calculating a field strength from a static 
assemblage of "charge" generators (again, whether it's gravitational or 
electromagnetic) and then examining the behavior and dynamics of the 
resulting fields.

First, I presume there is no 3D analog for StreamPlot?  So StreamPlot 
can only visualize two-dimensional cross-sections?

Second, I'd like to show a ContourPlot of the potential of some of these 
fields fields, but sometimes the equation of the field strength has to 
be numerically integrated (with NIntegrate) at each point rather than 
having a simple, closed-form solution that I could pump through DSolve 
to solve for the potential from the field strength.  Any suggestions here?

Third, sometimes I want to look at dynamics of particles responding to 
these fields, and I've seen numerical integration of the dynamics of 
closed-form fields.  But how do I tackle the numerical integration of 
the path of a particle responding to forces on it from a field when the 
field itself has to be numerically integrated at each point?

If this is all too abstract I'll give examples, but hopefully I'm making 
my intentions clear.  Thanks.

Erik Max Francis && max at &&
  San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis
   Tomorrow does not exist. Twenty tomorrows is a long time.
    -- Lady Mariko

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