Controlled Lagrangians and stabilization of discrete spacecraft with rotor

The method of controlled Lagrangians for discrete mechanical systems is extended to the problem of stabilization of the rotations of a spacecraft with a symmetric rotor. In particular, stabilization about its intermediate axis of inertia is considered. The Moser-Veselov discretization is used to obtain the discrete dynamics of the system. Stabilization conditions for the continuous model and its discretization are compared. It is shown that stability of the discrete system is sufficient for stability of its continuous counterpart but not vice versa.