Dynamics and Control of Tethered Satellite System in Elliptical Orbits under Resonances

Abstract

This paper studies resonance motions of a tethered satellite system (TSS) in elliptical orbits. A perturbation analysis is carried out to obtain all possible resonance types and corresponding parameter relations, including internal resonances and parametrically excited resonances. Besides, a resonance parametric domain is given to provide a reference for the parameter design of the system. The bifurcation behaviors of the system under resonances are studied numerically. The results show that resonant cases more easily enter chaotic motion than nonresonant cases. The extended time-delay autosynchronization (ETDAS) method is applied to stabilize the chaotic motion to a periodic one. Stability analysis shows that the stable domains become smaller in resonance cases than in the nonresonance case. Finally, it is shown that the large amplitudes of periodic solutions under resonances are the main reason why the system is difficult to control.