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Re: Phase Plane Diagrams in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg17468] Re: Phase Plane Diagrams in Mathematica
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sun, 9 May 1999 04:44:02 -0400
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <7gjfbc$cof@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

[I tried to reply to a similar posting a while back, but my response got
rejected because of what the software somewhere said was an invalid
thread.]

Take a look at the notebook HarmonicSink.nb at the URL 

 
http://umastr1.math.umass.edu/Courses/Math_431_Eisenberg/Files/files.html

on my differential equations course Web site.  It shows the technique --
combining a direction field plot with a plot of a solution curve in the
phase plane.

This could readily be extended to show enough phase plane solution
curves to give a reasonable phase portrait.  But the technique clearly
is tedious, in that the ParametricPlot used to draw a solution curve has
to be manually fine-tuned so as to restrict the t-interval lest the
curve stray outside the region of the direction field plot.  (If you
don't do that, then you could wind up with a nice solution curve but
with the entire direction field cramped down to a tiny portion of the
combined plot.)

The lovely package ODE that accompanies the text "Introduction to
Ordinary Differential Equations with Mathematica", by Gray, Mezzino, and
Pinsky (Springer-Verlag New York, 1997) has an easy way to plot families
of solutions in the phase plane parametrized by initial conditions. 
Packages and documentation are available at the Web site:

  http://math.cl.uh.edu/ode/3x/index.htm


Gary Reich wrote:
> 
> Does any one know of a way to produce Phase Plane Diagrams in mathematica?
> I need to construct a couple for my differntial equations class.


-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.       phone 413 549-1020 (H)
Univ. of Massachusetts                     413 545-2859 (W)
Amherst, MA 01003-4515


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