**Date:** Mon, 18 Oct 2004 14:34:23 -0400

**Author:** sampere

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

**Post:**

I'm glad you guys are taking care of the theory. I'm just happy to know

that pasta and clams are yummy!

You can find a java applet for anything. I'm still not a big fan of

'video game' physics.

Sam

Andrew Graham wrote:

> 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 11:28:43 2004