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

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.