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

**References**:**Phase Portrait***From:*herato <herato@gmail.com>