Stabilization and attitude of a triaxial rigid body by Lie group methods

This paper deals with the construction of algorithms which preserve the first integrals of a class of forced rigid motions, which retains a Hamiltonian structure, using Lie group methods such as those due to Lewis and Simo and Munthe-Kaas. For these mechanical systems, we also study the reconstruction of dynamical processes to describe the evolution of the orientation of the forced rigid body in space; for this we consider different algorithms to solve the kinematic equations. A comparison between these algorithms is made. Finally, we illustrate the numerical methods discussed here, studying the stabilization of the relative equilibrium corresponding to the stationary rotation about the intermediate axis in the presence of external torques about the minor axis.