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Re: Plotting Tajectories with Mathematica

  • To: mathgroup at
  • Subject: [mg17092] Re: Plotting Tajectories with Mathematica
  • From: Murray Eisenberg <murray at>
  • Date: Fri, 23 Apr 1999 02:32:21 -0400
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <7f1c7a$>
  • Sender: owner-wri-mathgroup at

In principle, combining a vector field plot and parametric plots of one
or more solution curves in the phase plane is no more or less
complicated than combining any other graphics objects:  create the plots
(giving each a name and probably using an option DisplayFunction ->
Identity to suppress display of the individual plots), then display them
overlayed via a Show expression (in which you need to use the option
DisplayFunction -> $DisplayFunction in case you used the previously
mentioned option for the individual plots).

To get satisfactory results, of course, you need to worry about such
things as the appropriate domain for the parameter t in the parametric
plot, so that if, say, the solution curve spirals outward, it actually
extends just to the edge of the plot range for the vector field.  If you
give too large a domain for the parameter, then the combined plot could
easily have the entire vector field scrunched in a little corner and a
really long solution curve sticking out!

For some examples, you might take a look at my course Web site

navigate to the Files page.  From there you can download some
Mathematica 3.0 notebooks with the sort of thing you asked about. 

Adam Price wrote:
> I am able to plot Vector Fields, using the standard add-on package.  I
> would like to overlay a few sample trajectories, using initial conditions
> of my choosing.  Are there any home-made packages for this out there?  Any
> easy way to do it?
> Thank you,
> Adam

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

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