An Orbiting Dumbbell with a Variable Mass Distribution: Dynamics and Control

The plane orbital motion of a dumbbell-shaped body of variable length in the central field of attraction is considered. It is assumed that the mass of the dumbbell is concentrated at its end points. The attitude motion is considered within the so-called “satellite approximation,” when the center of mass of the dumbbell moves in an unperturbed elliptical Keplerian orbit. The laws of changing the length of the dumbbell have been found, which make it possible to implement certain prescribed classes of its motion around the center of mass. In the general case, the chaotic nature of motion is detected numerically using the Poincaré map for the period.