充液航天器姿态稳定分析的Casimir方法

充液航天器中的液体燃料晃动将可能导致航天器姿态不稳定性现象的发生．本文采用哈密顿动力学方法研究了半充液航天器姿态运动的稳定性问题．首先将晃动液体等效为弹簧质量块力学模型，建立了液体晃动与航天器姿态多体耦合动力学系统的哈密顿方程，并进一步推导了与耦合动力学系统相关的Casimir函数；借助于Casimir函数并采用李亚普诺夫稳定性理论推导出耦合系统的稳定性和非稳定性条件，最后给出了数值仿真结果及相关结论．

Casimir method for attitude stability analysis of liquid-filled spacecraft

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.