Periodic orbits, manifolds and heteroclinic connections in the gravity field of a rotating homogeneous dumbbell-shaped body

This paper studies local and global motion in the vicinity of a rotating homogeneous dumbbell-shaped body through the polyhedron model. First, a geometric model of dumbbell-shaped bodies is established. The equilibria points and stabilities thereof are analyzed under different parameters. Then, local motion around equilibrium points is investigated. Based on the continuation method and bifurcation theory, several families of periodic orbits are found around these equilibria. Finally, to better understand the global orbital dynamics of particles around a dumbbell-shaped body, the invariant manifolds associated with periodic orbits are discussed. Four heteroclinic connections are found between equilibria. Using Poincaré sections, trajectories are designed for transfers between different periodic orbits. Those trajectories allow for low-energy global transfer around a dumbbell-shaped body and can be references for designing reconnaissance orbits in future asteroid-exploration missions.