The equilibria and periodic orbits around a dumbbell-shaped body

This paper investigates the equilibria, their stability, and the periodic orbits in the vicinity of a rotating dumbbell-shaped body. First, the geometrical model of dumbbell-shaped body is established. The gravitational potential fields are obtained by the polyhedral method for several dumbbell-shaped bodies with various length-diameter ratios. Subsequently, the equilibrium points of these dumbbell-shaped bodies are computed and their stabilities are analyzed. Periodic orbits around equilibrium points are determined by the differential correction method. Finally, in order to understand further motion characteristic of dumbbell-shaped body, the effect of the rotating angular velocity of the dumbbell-shaped bodies is investigated. This study extends the research work of the orbital dynamics from simple shaped bodies to complex shaped bodies and the results can be applied to the dynamics of orbits around some asteroids.