Characterization of out-of-plane libration of tethered satellite systems in elliptical orbits

Abstract

This paper investigates the dynamic behavior of a tethered satellite system in an elliptical orbit as the tethered subsatellite is deployed from a mother satellite at an out-of-plane angle while maintaining the tether at a constant in-plane pitch angle by a predefined control force acting on the subsatellite. A variable-length pendulum model is employed to describe the purely out-of-plane tether deployment dynamics, from which an analytical tether deployment control law is derived. The stability condition of the analytical control law is examined by Floquet theory. The corresponding analytical deployment law is asymptotically stable, and the requirement for a positive tension control input is guaranteed to ensure the controllability of the tether system. Following deployment, the critical conditions for the out-of-plane libration of the tethered subsatellite to become chaotic during the station-keeping phase are examined. Finally, simulation results reveal that the proposed approach can effectively and rapidly identify periodic, quasiperiodic, and chaotic motions using bifurcation diagrams, which provides valuable insights for enhancing the stability and reliability of such tethered satellite systems.