Casimir method for attitude stability analysis of liquid-filled spacecraft

Abstract

Sloshing is the phenomenon which is related with the free surface movement of fluid inside a container. In this paper, Hamiltonian dynamics method was used to study the stability of attitude motion for spacecraft with liquid sloshing in tank .In this article, the equivalent mass-spring mechanical model was used to analogue the liquid sloshing dynamics which was coupled with spacecraft attitude dynamics. Hamiltonian equations and Casimir functions was found for the proposed dynamical model for the coupled multi-body liquid-filled spacecraft system. The stability conditions and instability conditions for attitude motion of partially liquid-filled spacecraft were derived by using Lyapunov function along with Casimir functions. Numerical result was presented to strengthen the derived results and to show the geometric illustration of the stable and unstable regions in parameters space.