Periodic Solutions and Controls of Tethered Systems in Elliptic Orbits

Abstract

In this paper we study the periodic solution of the librational motion of a tethered system in elliptic orbit and clarify its mechanical characteristics. Basic libration control toward the periodic solution is also presented. A tethered system is modeled as a rigid body, and a set of nonlinear equations of motion about the librational and the orbital motions is formulated. An approximated analytical solution is obtained through the Lindstedt perturbation method. The total mechanical energy is formulated, and it is shown that it has the minimum value when the librational and orbital motions coincide with the periodic solution. This means that the periodic solution is the minimum energy solution, and that the periodic solution in an elliptic orbit has the same significance as the equilibrium state in a circular orbit from the mechanical point of view. A libration control toward the periodic solution is also investigated, and the effectiveness of this control strategy is demonstrated by using the periodic on-off control through a thruster installed on the subsatellite.