Global asymptotic stabilization of a spinning top with torque actuators using stereographic projection

The dynamical equations for a spinning top are derived in which the orientation is specified by a complex variable using stereographic projection of Poisson's equations. Necessary and sufficient conditions for Lyapunov stability of the uncontrolled motion of a spinning top are given using the Energy-Casimir method. Control laws that globally asymptotically stabilize the spinning top to the sleeping motion using two torque actuators are then synthesized by employing techniques from the theory of systems in cascade form and generalized using Hamilton-Jacobi-Bellmann theory with zero dynamics.