In-Plane/Out-of-Plane Librations of a Tethered System in Elliptical Orbits

In-plane/out-of-plane librations of a tethered system in elliptical orbits are investigated. It is aimed to clarify the fundamental characteristics of libration of the tethered system subjected to orbital motion and atmospheric drag. Periodic solutions and their stability of a simplified 3-DOF model are analyzed, in which in-plane/out-of-plane librations and longitudinal elongation of the tether are considered. It is shown that the librations become asymptotically stable or unstable because of atmospheric drag. The effects of system parameters on stability are analyzed, and it is shown that the property of longitudinal elongation of the tether determines the nature of stability, that is, asymptotically stable or unstable. It is also shown that the property of atmospheric drag determines only the degree of stability. Results of direct numerical simulations show the validity of the results of stability analyses. Physical interpretation of the phenomena is also clearly shown.