Asymptotic stabilization of uniform motion in Hamiltonian systems

In some cases a desired motion can be described by two first integrals of the system with zero control input. These two integrals are used to construct Lyapunov function. The control is designed from the condition of decreasing Lyapunov function on the trajectories of the closed loop system. This control may be a priori bounded. This method is applied to stabilize rotating body beam, for damping the oscillations of blades of an elastic propeller, for stabilization of permanent rotation of a rigid body with fixed point and for stabilization of the uniform transition of a hanging pendulum on a cart.