Global asymptotic stabilization of the spinning top

Considers the problem of controlling a top in sleeping motion using two different actuation schemes. For a fixed-base top two actuators are assumed to provide forces at the center of mass in inertially fixed directions, while for a cart-mounted top two actuators are assumed to apply forces to the cart in inertially fixed directions. The controller for the cart-mounted top is obtained from the controller designed for the fixed-base top using D´Alembert´s principle. Both controllers are proved to be globally asymptotically stabilizing. For the uncontrolled fixed base top, necessary and sufficient conditions for Lyapunov stability of the sleeping motion are derived.