Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube

TL;DR

This paper explores the dynamics of a particle around a rotating cube, identifying equilibria, periodic orbits, and heteroclinic connections, which enhances understanding of orbits around irregular celestial bodies.

Contribution

It extends previous models by analyzing a rotating cube, calculating equilibria, and demonstrating the existence of complex orbit structures including heteroclinic connections.

Findings

Equilibria and their linear stability are determined.

Periodic orbits around equilibria are computed and analyzed.

Heteroclinic orbits connecting periodic orbits are numerically demonstrated.

Abstract

This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be considered as an extension of previous research work on the dynamics of orbits around simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates with backgrounds in celestial mechanics. In the synodic reference frame, the model of a rotating cube is established, the equilibria are calculated, and their linear stabilities are determined. Periodic orbits around the equilibria are computed using the traditional differential correction method, and their stabilities are determined by the eigenvalues of the monodromy matrix. The existence of homoclinic and heteroclinic orbits connecting periodic orbits around the equilibria is examined and proved numerically in order to understand the global orbit structure of the system. This study contributes to the investigation of irregular shaped celestial bodies that can be divided into a set of cubes.