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Stabilization of the desired uniform rotation in underactuated systems

In some cases the desired uniform motion may be described
by a pair of first integrals of the system with zero control input.
The linear-quadratic combination of these two integrals
is 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 chosen a priori bounded.
This method is applied to
stabilize circular motion of a satellite around gravitational center,
for stabilization inertia wheel pendulum and for swinging a pendubot.
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