Librational characteristics of a dumbbell modeled tethered satellite under small, continuous, constant thrust

Tether drag deorbit technology with chemical propulsion is an effective method of active removal of space debris, which is completely different from the traditional applications of tethered satellites. During flight in a non-Keplerian orbit, the tethered satellite is impacted by a compelling active thrust and presents complicated librational characteristics. In this article, based on a dumbbell model of tethered satellite, analytical first-order solutions of the librational angles of a tethered satellite are derived under a small, continuous, constant thrust in the transversal, tangential, radial and binormal directions. The librational characteristics of a tethered satellite are revealed for two conditions: (1) in-plane orbit transfer of an abandoned satellite and (2) adjustment of the orbital inclination of a satellite. Furthermore, the ranges of designed system parameters, such as initial geocentric distance, mass of the system, mass ratio between base satellite and objective satellite, tether length, and thrust acceleration, are analyzed for an orbit transfer. Afterwards, linear quadratic regulator based tension controllers are designed to damp out the librational angles and to achieve attitude stability of a tethered satellite. Numerical simulation results show that complicated librational characteristics of a tethered satellite under small, continuous, constant thrust are strongly influenced by the designed system parameters. In addition, the librational angles are controllable by a designed inhibitive controller for a set of given system parameters, which is useful for flight safety in maneuvering.