Symmetric and asymmetric dynamics of a tethered satellite in nontypical planes

Abstract

The dynamics of tethered satellite systems operating in typical planes (e.g., the orbital plane and the planes perpendicular to the orbital plane) has been well analyzed. However, studying the orbital system in nontypical planes might be more practical. Hence, this paper concentrates on the dynamic behaviors of a tethered system with two satellites in any plane, along with active out-of-plane suppressions. First, noninertial and inertial reference frames are introduced to build a billiard and a bead model for the original system. The low-dimensional model is applicable to efficient evaluation, while the high-dimensional model is more suitable for depicting the configuration changes of a flexible tether. Then, the in-plane motion stability in a transformed reference frame is examined via the Poincaré map. A numerical dynamic zone that depends on the system parameters and initial states is utilized to sketch the system spins, pendulum-like motions, and irregular oscillations. The simulation results demonstrate that the parameter zone is periodic. The symmetry and asymmetry of the dynamic forms are also presented. Finally, a corresponding relationship between model selection and dynamic behaviors is proposed.