Damping of out-of-plane oscillations of a spherical object during contactless transportation by an ion beam

This paper is devoted to the problem of space debris removal from near-Earth orbits. The ion-beam shepherd concept is used as the basis for this study. A spherical space debris object is transported by an ion beam generated by an active spacecraft engine. The relative motion of space debris with respect to an active spacecraft is studied. The active spacecraft is supposed to be a material point moving in a circular orbit. The center of mass of space debris can oscillate with respect to the orbit plane during transportation. The purpose of this study is to derive the optimal control law for the thrust force of an active spacecraft engine that provides the fastest damping of out-of-plane oscillations. The Bellman equation is used to develop the optimal control law. The numerical simulation of space debris deorbiting reveals the accuracy of the proposed control law. It is shown that periodic engine shutdown does not significantly increase the deorbiting time.