Swing principle in tether-assisted return mission from an elliptical orbit

The problem of a tether-assisted payload return from an elliptical orbit is considered in this study. In contrast to the existing works devoted to this issue, the article deals with a tether length control that provides a transfer of the payload into a descent trajectory from the tether rotation mode. Application of the swing principle for the tether control is investigated. The simplified mathematical model of the space tethered system is developed. It is shown that the stable limit cycle could exist under the considered control. The approximate analytical solution for this cycle is obtained. The stability of this solution is studied by the Lyapunov's theorems. The optimal control, which provides transfer of the payload into the descent trajectory with minimum perigee radius, is found as a result of the simulation series. It is shown that the tether should occur several turns before the payload separation. For example, in the YES-2 experiment, it is demonstrated that proposed control makes it possible to perform a payload return using a tether of considerably shorter length. The main conclusion of the paper is that the proposed scheme of the payload deorbit is more effective than the classical static or dynamic tether deployment schemes.