The dynamic instability analysis of electrodynamic tether system

Abstract

The libration motion of conductive tether in electrodynamic tether system had been demonstrated unstable inherently. This paper conducts a further dynamic analysis of the instability in electrodynamic tether system, specifically investigating the existence of periodic solution and equilibrium point, as well as exploring the condition for rapid instability in libration motion. The dumbbell model is employed to depict the in-plane and out-plane libration motion, and the parameter  is introduced to incorporate the influences of tether current and inclination. The critical ranges of  and out-plane angle that determine whether the libration motion will go tumbling quickly are derived analytically based on the existence condition of periodic solution and equilibrium point. The numerical simulations were conducted to demonstrate these analytical critical ranges, and the results show that the libration motion will become unstable quickly if the out-plane angle or  exceeds the critical range even under control strategy. This critical range of  and out-plane angle is a general conclusion applicable to any situation (within the limitation of the model considered in this study), which can be utilized in guiding the design of system parameters to avoid rapid instability of electrodynamic tether system.