Acquisition of a Desired Pure-Spin Condition for a Magnetically Actuated Spacecraft

IN THIS note, a rigorous proof of global exponential stability is derived for a magnetic control law that drives a rigid satellite toward a pure-spin condition around a prescribed principal axis of inertia with a desired angular rate ω d . In a recent paper [1], two of the authors of the present note proposed a proof of global asymptotic stability for a B-dot-like control law that detumbles a spacecraft by means of magnetic actuators only. In this framework, they proved that, in the presence of a time-varying magnetic field, the time derivative of the kinetic energy is strictly decreasing. The physical interpretation of the effects of the B-dot law allowed for the derivation of a criterion for selecting the gain that results in quasi-minimum detumbling time to zero angular speed.