Stability and control of a two-craft magnetic constellation

In this paper we derive the reduced dynamical equations of motion for a planar two-spacecraft magnetic formation. We will derive relative equilibrium conditions and solve them to obtain families of relative equilibria. It will be shown that the relative equilibria (there are exactly two families of equilibria) are unstable. Optimal linear feedback control will be employed to stabilize the relative equilibria. Open loop formation size change maneuvers will also be derived. Simulation results will be provided for all theoretical results presented in the paper.