Stability of Motion of a Tethered System when Towing Spacecraft with Propellant Outage

Abstract

The plane motion in a circular orbit of a tethered system consisting of a space tug and a nonoperational spacecraft with propellant outage is considered, and the system motion with respect to its center of mass under the action of the gravitational torque and a constant driving force of the space tug is studied. Lagrangian formalism is used to construct the nonlinear equations of motion and the first-order approximation equations. An analysis of the frequencies and mode shapes permits determining a combination of the system parameters for which the deviation angles of the tether and the towed object do not attain significant values. The results can be used to analyze the behavior and the choice of theparameters of the tethered transport systemintended for the space debriswithdrawal from the orbit (upper stages of launchers and nonoperational satellites).