This article focus on the rigid-liquid coupling dynamics of the spacecraft with arbitrary axisymmetrical tanks with curved walls and top. The carrier velocity potential function was obtained according to the motion equations of a representative point in the tank of spacecraft, and the relative velocity potential function can be expressed as Gauss hypergeometric series. The Hamilton's variational principle was applied to derive the governing equations of liquid sloshing based on the profile of hydrostatic shape of free liquid surface. The dynamic equations of modal coordinates were established through the Galerkin method. The state equations of coupled motion of main rigid platform of the spacecraft were deduced by using the Lagrange's equations in term of general quasi-coordinates. Thruster firing was actuated to the coupled system to analyze the rigid-liquid coupled dynamic behaviors. Computer numerical simulations was carried out to confirm the validity of the method developed in this paper.
