On the magnetic attitude control for spacecraft via the ε-strategies method

We develop a new approach to stabilization problems based on a combination of the Lyapunov functions method with local controllability properties. The stabilizability is understood in the sense of ε-strategies introduced by Pontryagin in the frame of differential games theory. To illustrate the possibilities of our approach we consider a satellite with two magnetic coils directed along its principal inertia axes. Its circular orbit is neither polar nor equatorial. We show that there exists an ε-strategy stabilizing an Earth pointing satellite, whenever the deviations from the equilibrium position are small enough.