Nullcline Analysis as a Tethered Satellite Mission Design Tool

Abstract

Tethered satellite systems have been proposed for many space mission applications due to the useful dynamics that can be generated in such systems. For instance, tethered satellite systems can be used to increase the orbital radius of low Earth orbit payloads using angular momentum transfer; another tethered satellite system proposal involves the use of a variable length, spinning tethered system to produce specific levels of artificial gravity in low Earth orbit. Increasing interest in tethered satellite systems necessitates a fundamental understanding of the dynamics of such systems. An analytic method of qualitatively describing the possible dynamics of a tethered satellite system is presented. This analysis is centered on the study of the sets of states at which at least one of the nondimensional time derivatives of the state variables is zero; these sets are known as the nullclines of a system and they bound regions of the phase plane in which tethered satellite behavior is similar. The qualitative analysis of the nullclines provides an explanation for, and suggests the controllability of, many types of tethered satellite behavior. A Tethered Artificial Gravity (TAG) satellite system is used as a canonical tethered system and the results derived are applied to this system. The utility of the described analytical method is demonstrated by using the method to characterize two different tethered satellite missions.