English

Chaotic dynamics of a bouncing coin

Dynamical Systems 2016-03-10 v1

Abstract

We study the dynamics of a bouncing coin whose motion is restricted to the two-dimensional plane. Such coin model is equivalent to the system of two equal masses connected by a rigid rod, making elastic collisions with a flat boundary. We first describe the coin system as a point billiard with a scattering boundary. Then we analytically verify that the billiard map acting on the two disjoint sets produces a Smale horseshoe structure. We also prove that any random sequence of coin collisions can be realized by choosing an appropriate initial condition.

Keywords

Cite

@article{arxiv.1603.02783,
  title  = {Chaotic dynamics of a bouncing coin},
  author = {Ki Yeun Kim},
  journal= {arXiv preprint arXiv:1603.02783},
  year   = {2016}
}
R2 v1 2026-06-22T13:06:59.824Z