Study of dynamical stability of tethered systems during space tug maneuvers

The dynamics of a space tether system composed of one active spacecraft, an uncontrolled large debris (e.g., a defunct satellite), and a visco-elastic tether connecting the two bodies are investigated in this paper. The active spacecraft is assumed to be equipped with a propulsive system for carrying out a tug maneuver that forces the orbital decay of the debris. The dynamical stability and the eigenfrequencies of the tethered system under the action of the thrust are investigated with both numerical and analytical models. A more complex numerical lumped-masses model provides the reference to validate the results hailing from the simplified models. Simplified models of orbital decay, tether, and debris attitude motions were derived using the Clohessy-Wiltshire equations. The results obtained with the simplified models fit very well with those from the lumped-masses model for a wide range of initial conditions. Thanks to the analytical models two resonance conditions were found, both of them affecting the attitude dynamics of the debris, that could represent a serious issue for the safety of the tug maneuver. Also, an instability mechanism that could induce the dual mass system to rotate around its center of mass under certain conditions was identified. These findings make it possible to pinpoint the set of initial conditions of the tethered system at the beginning of the thrust event that provides a dynamically stable tug maneuver for different configurations of the system (e.g., low/high thrust, stiff/elastic tethers).