Stability of Electrodynamic Tethers in a Three-Body System

Abstract

The dynamics of an electrodynamic tether orbiting in a three-body gravitational field near the equilibrium positions of the system is analyzed. First, the perturbed classical three-body problem is derived in general terms; then, the in-plane force perpendicular to the local vertical is analyzed in more detail because of its relevance to electrodynamic tethers. Because of the presence of electrodynamic forces, the locations of equilibrium points are modified from their classical Lagrangian positions (that are valid for a null electrodynamic force) and finally disrupted as the electrodynamic force increases.A linear variational analysis is carried out to characterize themotion of the tethered system around the perturbed equilibrium locations and to compute the variation of the eigenfrequencies versus the intensity of the electrodynamic force. The study of small-amplitude motion about the perturbed equilateral positions has shown the existence of in-plane orbits (Lyapunov) and out-of-plane orbits (Lissajous and halo types) around those points. Large-amplitude orbits, which include nonlinear effects, have been studied using numerical integration of the equations of motion. Numerical tests have proven that when the higher of the two eigenfrequencies is excited, the trajectory is stable and converges toward the equilibrium point. The analysis is of immediate use to the orbit design of motion around perturbed Lagrangian points of electrodynamic tethers.