Stabilization of a rotating rigid body by the energy momentum method

The authors discuss the stabilization by feedback control of a rigid body uniformly rotating about an arbitrary axis. They consider a class of feedback laws that depend on a parameter matrix W, which is nonsingular and symmetric. It is shown that under this class of feedback laws, the closed loop system is Hamiltonian and represents the motion of a generalized rigid body. For such systems the energy-momentum method enables determination of feedback gains which ensure the stability for the closed loop system. Several examples are used to demonstrate the methodology