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

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