Not chaos

Classical Mechanics Level 2

The gas of non-interacting molecules actually provides a good example with which to discuss chaotic vs. non-chaotic systems. An "easier", but still similar system to our gas is billiard balls on a table. This system is 2-d, rather than 3-d, and is much easier to visualize.

Our billiard table is square with corners at (-2,2), (2,2), (2,-2), and (-2,-2), where I measure everything in meters. It's a wonderful billiard table as the balls have no friction with the table and bounce off elastically from the walls. Hence if I start a ball rolling, it rolls forever.

A simple problem first: I start a ball rolling at the origin with velocity (0,1) m/s. How long does the ball take to return to the origin in seconds?

You can read this Introductory note - What is Chaos anyway?


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