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arXiv · 2411.10324

One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction

Théophile Dolmaire·Eleni Hübner-Rosenau
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Abstract

We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient $r$, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision pattern, proving that it can be realized, despite its instability. We prove that we can associate to the four-particle dynamical system another dynamical system of smaller dimension, acting on $\{1,2,3\} \times \mathbb{S}^2$, and that encodes the collision orders of each trajectory. We provide different representations of this new dynamical system, and study numerically its $\omega$-limit sets. In particular, the numerical simulations suggest that the orbits of such a system might be quasi-periodic.

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Théophile Dolmaire, Eleni Hübner-Rosenau. 2024-11-15. One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction. https://doi.org/10.1088/1361-6544%2Fadc9ee

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