A topological obstruction to continuous global stabilization of rotationalmotion and the unwinding phenomenon

We show that a continuous dynamical system on a state space that has the st ructure of a vector bundle on a compact manifold possesses no globally asym ptotically stable equilibrium. This result is directly applicable to mechan ical systems having rotational degrees of freedom. In particular, the resul t applies to the attitude motion of a rigid body. In light of this result, we explain how attitude stabilizing controllers obtained using local coordi nates lead to unwinding instead of global asymptotic stability. (C) 2000 El sevier Science B.V. All rights reserved.