Stability analysis of in-plane and out-of-plane periodic motions of electrodynamic tether system in inclined elliptic orbit

This paper analyzes the stability of in-plane/out-of-plane motion of electrodynamic tether (EDT) systems in elliptic and inclined orbits. The chaotic librational motion of an EDT system in inclined elliptic orbits has been studied extensively and it is believed that delayed feedback control cannot stabilize the librational motion of an EDT in an inclined and elliptic orbit with high eccentricity. Contrary to previously published results, the analytical results in this paper reveal that delayed feedback control can stabilize the in-plane/out-of-plane coupling librational motion of EDT systems in inclined elliptic orbits with high eccentricity to a periodic motion because the in-plane and out-of-plane coupling motions do not have the odd number condition if the electric current can flow on tether in both direction, and appropriate control gains are chosen. The validity of the stability analyses in this paper is confirmed through numerical simulations in which a delayed feedback control with appropriate control gains is applied to the in-plane/out-of-plane coupling periodic motion of an EDT system in inclined elliptic orbit with high eccentricity.