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37 votes
6 answers
3k views

Billiard dynamics under gravity

Has the dynamics of billiards in a polygon subject to gravity been studied? What I have in mind is something like this:            Still Snell's Law ...
Joseph O'Rourke's user avatar
33 votes
4 answers
3k views

Does there exist a shot in ideal pocket billiards?

Assume you have one shot with the cue ball in pocket billiards (a.k.a. pool), with the game idealized in that no spin is placed on the cue ball in the initial shot, all collisions between billiard ...
Joseph O'Rourke's user avatar
14 votes
2 answers
1k views

Polygonal billards programs

I'm looking for software that will give billiard trajectories in arbitrary plane polygons. After much work I was able to produce this figure. (source) It was a good exercise, but at this point I ...
john mangual's user avatar
  • 22.8k
7 votes
2 answers
274 views

Well-definedness of single-particle smooth billiards flow

Single-particle billiards systems in a domain with corners, or multi-particle billiards in a domain with smooth boundary, can exhibit singularities in finite time. (The former phenomenon is well known;...
James Propp's user avatar
  • 19.7k
5 votes
0 answers
166 views

Pocket billiards with balls in general position

There were at least two earlier MO questions about ideal pocket billiards. (Ideal: frictionless, perfectly elastic collisions.) Perfectly centered break of a perfectly aligned pool ball rack. Does ...
Joseph O'Rourke's user avatar
5 votes
3 answers
2k views

Dense orbits in billiards

This should be true in a more general setting, but for simplicity consider billiards that are connected, compact subsets of the plane with boundary $C^2$ except at finitely many points. A ball (or a ...
Zatrapilla's user avatar