Existence of periodic motions of a tether trailing satellite

摘要

Tethered satellite systems are becoming more widely used in space explorations. In this analytical study, the dynamics of a satellite trailing a tether are addressed. More precisely, we derive the conditions for existence of periodic motions about the relative equilibrium states of the tethered system. The system is considered to be affected by the atmospheric drag and nonspherical Earth. The mathematical proof of the existence result is based on the Leray–Schauder degree theory. Main conclusions can be easily generalized for any bounded forcing and/or forces with linear growth.