Electrodynamic Tethers Under Forced-Current Variations Part I: Periodic Solutions for Tether Librations

摘要

Varying the current in electrodynamic tethers provides a means for manipulating the orbits of spacecraft. Thesenvariations can induce unstable librational motion of the tether. Periodic solutions of electrodynamic tethers undernforced currents are studied, which provide a reference trajectory for feedback control of the tether librations duringnorbit transfer. The tether is treated as a dumbbell, and periodic solutions are obtained by means of the Legendrenpseudospectral method. The technique provides the stability characteristics of the solutions by application ofnFloquet’s theory. Five different current profiles suitable for orbital maneuvering are used to obtain periodicnsolutions. An energy-rate feedback controller is applied to stabilize the dumbbell librations around the time-varyingnreference trajectory. The results show that sinusoidal and cosine currents with frequencies equal to that of the orbitnare neutrally stable for some orbit inclinations, whereas a cosine current with frequency twice that of the orbit isnunstable, with the degree of instability growing with the current amplitude.