Asymptotic stabilization of the heavy top using controlled Lagrangians

In this paper we extend the previous work on the asymptotic stabilization of pure Euler-Poincaré mechanical systems using controlled Lagrangians to the study of asymptotic stabilization of Euler-Poincaré mechanical systems such as the heavy top

Reduction of Controlled Lagrangian and Hamiltonian Systems with Symmetry

We develop reduction theory for controlled Lagrangian and controlled Hamiltonian systems with symmetry. Reduction theory for these systems is needed in a variety of examples, such as a spacecraft with rotors, a heavy top with rotors, and underwater vehicle dynamics. One of our main results shows the equivalence of the method of reduced controlled Lagrangian systems and that of reduced controlled Hamiltonian systems in the case of simple mechanical systems with symmetry