Non-linear dynamics and chaos control of a damped satellite with partially-filled liquid

The dynamic behaviors of a damped satellite with partially-filled liquid which is subjected to external disturbance are studied in this paper. The Lyapunov direct method is used to obtain conditions of stability of the equilibrium point of the system. A co-dimension one bifurcation analysis for the autonomous system is carried out near the degenerate point. It is found that Hopf bifurcation occurs in the system by center manifold theory. By applying numerical results, phase diagrams, power spectrum, Poincare maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameter changes in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Finally, several methods, the delayed feedback control, the addition of constant motor torque, the addition of periodic force, and adaptive control algorithm are used to control chaos effectively. (C) 1998 Academic Press.