Relative dynamics of charged spacecraft in a magnetic field applied to formation flight

We consider several charged spacecraft configurations around a leader spacecraft provided with an artificial magnetic field. In all configurations the nominal orbits are chosen to be about the relative equilibrium points of the reference model. Using a linear quadratic regulator controller, we find that controllability is possible in most of the cases, and it is strongly related to the stability of the equilibrium point which, in turn, depends on the orbit of the leader and the rotation rate of its magnetic dipole. The dynamical model considered shows a great potential for future formation flying applications since both, the establishment and maintenance of the configurations, can be managed by merely adjusting the charge on the follower spacecraft. No additional control variables are needed.