Homoclinic chaos in the Hamiltonian dynamics of extended test bodies

TL;DR

This paper investigates how finite-size effects and shape changes in extended bodies can induce chaos in Hamiltonian systems, providing new insights beyond traditional external perturbations, with applications to classical potentials.

Contribution

It introduces a novel mechanism for chaos in Hamiltonian dynamics caused by shape variations of extended bodies, expanding understanding beyond external perturbations.

Findings

Shape changes can induce chaos in Hamiltonian systems.

Chaotic regions appear around unperturbed orbits due to shape deviations.

Applications demonstrated in Duffing, Yukawa, and Kepler potentials.

Abstract

There is a long tradition of studying chaotic trajectories in systems whose integrability is broken by means of an external perturbation. Here we explore a different route to chaos, in the dynamics of extended bodies, which arises due to finite-size corrections to the otherwise integrable motion of a test particle. We find that cyclic changes in the overall shape of the body may lead to the onset of chaos. This is applied to the Duffing and Yukawa potentials. For Kepler's potential, periodic deviations from spherical symmetry give rise to chaotic regions around the unperturbed parabolic orbit.