GLOBAL ASYMPTOTIC STABILIZATION OF THE SPINNING TOP

Abstract

SUMMARY We consider the problem of controlling a top to the sleeping motion using two different actuation schemes. For a fixed‐base top two actuators are assumed to provide forces at the centre 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. For the case in which there is only one force actuator, locally asymptotically stabilizing control laws that drive the fixed‐base top to the sleeping motion are also obtained.