Inst. Prikl. Mat. Mekh., Ul. Rozi-Luxemburg 74, 340114 Donetsk-114, Ukraine

Summary: The attitude of a satellite is often controlled by reactive forces requiring some additional energy. But sometimes it can also be stabilized by means of a damped oscillator moving inside the satellite. This procedure does not require additional energy and is called "passive stabilization". Moreover the relative motion of the oscillator 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.