Bifurcation Diagrams and Generalized Bifurcation Diagrams for a rotational model of an oblate satellite

TL;DR

This paper analyzes the bifurcation structures and chaos in a rotational model of an oblate satellite, focusing on Saturn's moon Hyperion, revealing fractal and chaotic behaviors through Lyapunov exponents and recurrence times.

Contribution

It introduces bifurcation and generalized bifurcation diagrams for the satellite model, highlighting the fractal nature of chaos and quasi-periodic windows specific to Hyperion.

Findings

Largest Lyapunov exponent shows fractal structure.

Most parameter values lead to chaotic rotation.

Recurrence time diagrams explain chaos emergence.

Abstract

This paper presents bifurcation and generalized bifurcation diagrams for a rotational model of an oblate satellite. Special attention is paid to parameter values describing one of Saturn's moons, Hyperion. For various oblateness the largest Lyapunov Characteristic Exponent (LCE) is plotted. The largest LCE in the initial condition as well as in the mixed parameter-initial condition space exhibits a fractal structure, for which the fractal dimension was calculated. It results from the bifurcation diagrams of which most of the parameter values for preselected initial conditions lead to chaotic rotation. The First Recurrence Time (FRT) diagram provides an explanation of the birth of chaos and the existence of quasi-periodic windows occuring in the bifurcation diagrams.