On Passive Stabilization in Critical Cases

The attitude of a satellite is often controlled by reactive forces requiring some additional energy. But it can also be stabilized by means of some subsystem of the satellite moving in a nonideal fluid as an oscillator with damping. This does not require additional energy and is called ‘‘passive stabilization.’’ Moreover the relative motion tends asymptotically to zero together with the satellite finding the desired position. Here we consider passive stabilization for hamiltonian systems from a mathematical point of view and show that stabilization can sometimes be obtained by nonlinear terms. As an example, we consider passive stabilization of a simple pendulum