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.Comment: 29 pages, 16 figures, accepted for publication in Astrophysics &
Space Scienc