Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 119, 13 pages      arXiv:1810.05777      https://doi.org/10.3842/SIGMA.2020.119

Counting Collisions in an $N$-Billiard System Using Angles Between Collision Subspaces

Sean Gasiorek
School of Mathematics and Statistics, Carslaw F07, University of Sydney, NSW 2011, Australia

Received July 24, 2020, in final form November 10, 2020; Published online November 21, 2020

Abstract
The principal angles between binary collision subspaces in an $N$-billiard system in $d$-dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of collisions in the planar 3-billiard system problem. Comparison of this result with known billiard collision bounds in lower dimensions is discussed.

Key words: mathematical billiards; angles between subspaces; counting collisions.

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