**Date:** Mon, 18 Oct 2004 13:44:03 -0400

**Author:** Andrew Graham

**Subject:** Re: localized energy mode demo, i.e pendulum revisited

**Post:**

Andrew Dougherty wrote:

>On Mon, 18 Oct 2004, Andrew Graham wrote:

>

>

>

>>Thanks for sharing this. The physical model you describe is the basis

>>for the famous Sine-Gordon wave equation. This is closely akin to the

>>area of theoretical physics that I work in. The kink-antikink solutions

>>are well studied, and represent the "particle-antiparticle" pair created

>>when one pendulum goes through a full rotation and back to the

>>equilibrium position, producing two stationary twists along the row of

>>pendula. ( I have a similar demo that I copied from one made by Dick

>>Berg.) However, the solution you describe is a small oscillation effect

>>and very interesting. Do you have a reference to a publication

>>discussing this effect? There is probably an analogous solution in the

>>system I study.

>>

>>

>

>Offhand, it sounds like an example of FPU (Fermi, Pasta, and

>Ulam) Recurrence. There's a nice simulation of this in the Wiley CUPS

>series "Waves and Optics Simulations" by Antonelli, Christian, Fischer,

>Giles, James, and Stoner. There are probably nice Java applets posted

>somewhere on the web to do the same thing these days.

>

>

>

Andrew,

Thanks for that clarification. You are correct that the apparatus Sam

described is an FPU model. I should have said that this is the discrete

model that gives, in the continuum limit (as the separation between

adjacent pendula goes to zero), the Sine-Gordon wave equation. My

research begins with a discrete linear lattice of masses connected with

springs, and in the continuum limit gives the Klein-Gordon wave equation.

andy graham

From sampere@physics.syr.edu Mon Oct 18 11:22:49 2004