View Single Post
Old 03-01-2004, 02:58 PM
Mathochist Mathochist is offline
Join Date: Feb 2004
Location: New Orleans, LA
Posts: 3,031
Originally Posted by MikeS
And even that goes out the window if you add time-dependence of the equations of motion (e.g. a pendulum with a periodic driving force is chaotic.)

Note that having a phase space dimension of three or greater doesn't guarantee chaos, though; you also need some non-linearity in the system, and even then it's not certain.
A damped driven pendulum can be chaotic, depending on the parameters. I used up tons of my undergraduate university's computer time making movies of period-doubling cascades for Jim Yorke back when I thought I might make my name in chaos.

Anyhow, it's a great example of a perfectly simple classical mechanical system that still is completely unpredictable for certain parameter values.