Robust stabilization of a heavy top

This paper investigates the robust stabilization of relative equilibria. The motivating example is that of a heavy top. For the heavy top conditions which ensure the robust stabilization of the system are derived and discussed. These conditions generalize previous results for the rigid body. These conditions are then examined in the case of structured uncertainty in the mass and inertia properties of the top. Bounds are obtained for the family of stabilizing feedback gains and the corresponding error in the rotation axis is investigated. These results are then applied to the specific example of a heavy top with a mass imbalance spinning below critical velocity