Periodical Motion of a Tethered Satellite System around Collinear Libration Points

This paper studies the motion of a rotational tethered satellite system flying around collinear Lagrangian points of the Earth-Moon system. Equations of spatial motion of the mass center and the tether libration are deduced, but only the planar motion with constant rotation rate is discussed. First, the equation of the mass center is simplified and solved analytically for the scenario where the system is moving in the neighborhood of the libration point. The analytical solution indicates that both a bounded solution and periodical solution exist. A fully nonlinear dynamics analysis is then performed. A numerical method combining continuation and piecewise differential corrections is applied to obtain the periodical solution. Tether tension is also investigated. Simulation results validate the effectiveness of the proposed numerical method and the existence of the periodical orbits. The influence of parameters, such as spin rate, mass ratio of end satellites, and tether length are analyzed.