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MathGroup Archive 2007

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Re: Phase Portrait

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76263] Re: [mg76209] Phase Portrait
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 18 May 2007 06:28:09 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200705171058.GAA02483@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Yes!  In Mathematica 6.0 it's very easy:

   << EquationTrekker`
   << PhysicalConstants`
   g = AccelerationDueToGravity*Second^2/Meter; (* remove units *)
   EquationTrekker[y''[t]+(g/L y[t])Sin[y[t]]== 0,
          y,{t,0,20},TrekParameters->{L->1}]

This opens a window in which by right-clicking, you almost instantly get 
the trajectory for the point where you clicked.  So create as many 
trajectories as you wish.  And with the new 2D drawing tools, you can 
annotate the phase portrait, insert coordinates of points, etc.

[The group does not send out attachments.  I have put the graphic on
 one of my servers at http://smc.vnet.net/mgattach/murray.jpg - moderator]

See the attached screenshot.  I let EquationTrekker use its default 
colors for the various trajectories, but you may choose each color 
yourself, interactively.

Notice the option TrekParameters used above. The pendulum length L can 
be changed using the slider, and the trajectories will automatically 
change for the new value of L.

herato wrote:
> Hi!
> I would like to plot a simple phase portrait of some standard equation
> such as the pendulum .
> 
> How to do it?
> 
> It is completely equivalent to plot sublevels of the Hamiltonian, but
> in this case Mathematica does not plot the separatrix.....
> 
> 
> Thanks a lot!!!!
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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