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Results tagged with billiards
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Billiards are a class of dynamical systems in which a point particle moves uniformly in a domain $D\subset \mathbb{R}^d$ except for mirror-like reflections from the boundary. Varying $D$ leads to examples satisfying many ergodic properties. Billiards enhance visual explanations of dynamical concepts to students and the general public. There are many applications in physics and image processing. The free motion and/or reflection rule may be generalized.
10
votes
Billiard dynamics under gravity
As Willie Wong pointed out early on in the comments to the original problem, conservation of energy applies to the billiard ball in the tilted (or untilted) square, and this in itself can prevent the …
- 5,432
18
votes
Accepted
Billiard dynamics under gravity
As fedja notes in the comments, the bounces off the right and left walls can be accounted for by unfolding the unit square into a horizontal strip, so the trajectories can be viewed as the parabolic a …
- 5,432