Stability and chaos of a damped satellite partially filled with liquid

The stability and chaotic motions of a damped satellite partially filled with liquid which is subjected to external disturbance are investigated in this paper. With linearization analysis, the stability of the two non-trivial equilibrium points is studied. The homoclinic and heteroclinic orbits are found by using the undetermined coefficient method, and the convergence of the series expansions of these two types of orbits is proved. It analytically demonstrates that there exist homoclinic orbits of the Si’lnikov type that join the two non-trivial equilibrium points to themselves, and therefore smale horseshoes and the horseshoe chaos occur for this system via the Si’lnikov criterion. In addition, there also exists a heteroclinic orbit connecting the two non-trivial equilibrium points. Numerical simulations are also given, which verify the analytical results. The system can be chaotic through period-doubling bifurcations as the amplitude of the external disturbance varies, and backward period-doubling bifurcations as the angular momentum of the rotor varies.