Playing with numerically integrated fields?
- To: mathgroup at smc.vnet.net
- Subject: [mg97648] Playing with numerically integrated fields?
- From: Erik Max Francis <max at alcyone.com>
- 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
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 alcyone.com && http://www.alcyone.com/max/
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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