Stabilizing the Motion of a Low-Orbit Electrodynamic Tether System

This paper considers the motion of a low-orbit electrodynamic tether system designed to raise the orbit of a small spacecraft or nanosatellites. The system operates in the thrust generation mode. The orbit is raised by the Ampere force resulting from the interaction of the conducting tether with the Earth’s magnetic field. The mathematical model of motion is constructed using the Lagrange method taking into account the effect of the distributed loads from the Ampere force and the aerodynamic forces on the tether. It is shown that the motion of the system relative to the center of mass is unstable if the current is constant. It is proposed to use a linear regulator to stabilize the motion of the system with respect to the local vertical. Bellman’s dynamic programming principle is used to synthesize the regulator.