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.
Cite
@article{arxiv.1603.02783,
title = {Chaotic dynamics of a bouncing coin},
author = {Ki Yeun Kim},
journal= {arXiv preprint arXiv:1603.02783},
year = {2016}
}