Dynamic stability of electrodynamic tethers in inclined elliptical orbits

Abstract

For a circular orbit, the local vertical rotates uniformly about the orbit normal, and it is a stable equilibrium position for, basically, any tether. For an elliptical orbit, however, the local vertical does not rotate uniformly and it is no longer an equilibrium position for the tether: the librations dynamics become excited even if the tether is left at rest along the local vertical. Instead of stable equilibrium positions, the governing equations have periodic solutions. For an electrodynamic tether, the equilibrium positions along the local vertical do not exist even in the circular case. Using simple models to describe the Earth magnetic ?eld and the tether current, the governing equations also have periodic solutions instead of equilibrium positions. The goal of this paper is to analyze the e?ects of the combined action of these two forcing terms: the eccentricity of the orbit and the electrodynamic forces. We detect new periodic solutions and analyze their stability properties, which provide the dynamic stability of the system.