Long-Term Libration Dynamics and Stability Analysis of Electrodynamic Tethers in Spacecraft Deorbit

Abstract

Electrodynamic tether systems orbiting the Earth are prone to libration instability because of periodic changes in the geomagnetic field, plasma density, and lunisolar gravitational attractions in addition to nonperiodic changes resulting from the irregularity of the geomagnetic field, inhomogeneity of the Earth, and solar pressures. The long-term orbital and libration dynamics of a bare electrodynamic tether in deorbiting obsolete satellites is investigated by considering space environmental perturbations of current-induced electrodynamic force, atmospheric drag, Earth’s oblateness, irregularity of the geomagnetic field, variable space plasma density, solar radiation pressure, and lunisolar gravitational attractions. The electrodynamic tether is assumed to be rigid and the tethered spacecraft is modeled as a lumped mass. The study shows by numerical simulation that the out-of-plane libration is the primary source of libration instability in inclined orbits, which destabilizes the in-plane libration through nonlinear modal coupling. Accordingly, a simple stability criterion for current on/off switching control is derived from the libration energy of the tether to stabilize the out-of-plane libration by limiting the roll angle amplitude to a preset range. This in turn stabilizes the in-plane libration. The control requires only the feedback of the maximum roll angle with a minimum interval for current on/off switching imposed to avoid excessive current switching. The effectiveness of the control strategy has been demonstrated by analyzing the libration dynamics of electrodynamic tether with and without the current regulation in deorbiting satellites. Numerical results show that this approach is very effective in stabilizing both in-plane and out-of-plane libration of a tethered system subjected to periodic and nonperiodic perturbations.