Nullcline Analysis as an Analytical Tethered Satellite Mission Design Tool

Tethered satellite systems have been proposed for many space mission applications due to the useful dynamics that can be generated with relatively low fuel expenditures. 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 for 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. For the purposes of this paper, a tethered artificial gravity 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.

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