Re: Phase Plane Diagrams in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg17466] Re: Phase Plane Diagrams in Mathematica
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Sun, 9 May 1999 04:44:01 -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