Abstract
We give a new and elementary proof that the number of elastic collisions of a finite number of balls in the Euclidean space is finite. We show that if there are n balls of equal masses and radii 1, and at the time of a collision between any two balls the distance between any other pair of balls is greater than n−n, then the total number of collisions is bounded by n(5/2+ε)n, for any fixed ε > 0 and large n. We also show that if there is a number of collisions larger than ncn for an appropriate c > 0, then a large number of these collisions occur within a subfamily of balls that form a very tight configuration.
Original language | English |
---|---|
Pages (from-to) | 373-392 |
Number of pages | 20 |
Journal | Journal of the London Mathematical Society |
Volume | 101 |
Issue number | 1 |
DOIs | |
Publication status | Published - 30 Aug 2019 |
Keywords
- 37D50 (primary)
- 70F35 (secondary)
ASJC Scopus subject areas
- Mathematics(all)