On Passive Stabilization in Critical Cases

Abstract

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. ᮊ 2000 Academic Press

Asymptotical stability of the motion of mechanical systems with partial energy dissipation

“…The linear approximation has purely imaginary roots, and we get the critical case in Lyapunov sense [39,40]. For example, such a situation takes place for the system shown in Fig.…”

Nonlinear analysis on purely mechanical stabilization of a wheeled inverted pendulum on a slope

“…Extensive studies have been reported on the passive dynamic walking, including experimental development of passive walkers [1][2][3] and nonlinear analyses of passive dynamic walking based on simplified models [4][5][6]. Early insights into the use of such passivity can also be found in the study of passive gravity-gradient attitude stabilization [7][8][9][10] wherein the alignment of one axis of a satellite along the earth's local vertical direction was achieved without the use of active control elements.…”