Libration control of electrodynamic tethers in inclined orbit

Any electrodynamic tether working in an inclined orbit is affected by a dynamic instability generated by the continuos pumping of energy from electromagnetic forces into the tether attitude motion. To overcome the difficulties associated with this instability, two control schemes have been analyzed. In both cases the background strategy is the same: we add appropriate forces to the system with the aim of converting an unstable periodic orbit of the governing equations into an asymptotically stable one. The idea is to take such a stabilized periodic orbit as the starting point for the operation of the electrodynamic tether. In the first case, the unstable periodic orbit is taken as a reference orbit. In the second one, we use a delay feedback control scheme that has been used successfully in problems with one degree of freedom. To obtain results with broad validity, some simplifying assumptions have been introduced in the analysis. Thus, we assume a rigid tether with two end masses orbiting along a circular, inclined orbit. We also assume a constant tether current that does not depend on the attitude and orbital position of the tether, and the Earth's magnetic field is modeled as a dipole aligned with the Earth's rotation axis.