Analysis of librational and vibrational characteristics for tethered systems during orbital transfer in plane

The center of mass of a tethered system is in a non-Keplerian orbit during orbital transfer, which leads to a complicated dynamic behavior of the system and affects the normal operation of the mission satellite. Thus, it is of great theoretical and practical significance to study the librational and viberational characteristics of a tethered system. According to its complex nonlinear and strong coupling, an attitude dynamic equation of the tethered system is established on the basis of the momentum theorem; and against the background of deorbiting in the tangential direction, the trajectory of the center of mass is obtained. Based on the analysis of the bifurcation of the in-plane angle, the first-order analytical solutions of librational angles are derived. Then, a typical lumped mass model is introduced to study the longitudinal and transverse vibration of the tether. Furthermore, the coupling effects between the tether librational and vibration characteristics are analyzed. Numerical simulation results indicate that during orbital transfer, librational angles maintain a uniform-amplitude pendular motion around the equilibrium position at a specific angular frequency determined by factors such as the length of the tether, the thrust acceleration and the geocentric distance. It may result in resonance of the librational angle when the pendular motion frequency of the in-plane angle approaches the angular frequency of the orbit, and a great transverse motion also occurs during orbital transfer.