Dynamics of bouncing convex body

Xiaoming Zhang, Denghui Li, Celso Grebogi and Xianbin Liu

Chaos, Solitons & Fractals, 2024, vol. 183, issue C

Abstract: We consider a dynamical system that describes a convex planer body with a smooth boundary, which falls under the influence of gravity and is elastically reflected upon hitting a wall. Under suitable restriction on the system’s parameters, the system is equivalent to a billiard problem within a cylinder. We prove that the dynamics of the system is intimately linked to a variational problem, corresponding to a twist map. Moreover, we utilise the established variational method to investigate the stability of trivial periodic orbits and near-integrable dynamics when this planar body closely approximates a disc with its centre of mass at the geometric centre. Numerical results illustrates our mathematical findings and highlight the system’s intricate dynamics.

Keywords: Bouncing convex body; Twist map; Stability; Invariant tori; Integrable (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004478

DOI: 10.1016/j.chaos.2024.114895

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