Stability analysis of liquid filled spacecraft system with flexible attachment by using the energy–Casimir method

•The mechanical model of the coupled spacecraft system is constructed.•The nonlinear stability conditions are obtained by using the energy–Casimir method.•The stability region of the coupled system is obtained in the parameter space.

The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring–mass model, and flexible attachment was modeled as the linear shearing beam. The dynamic equations and Hamiltonian of the coupled spacecraft system were given by analyzing the rigid body, liquid fuel, and flexible appendage. Nonlinear stability conditions of the coupled spacecraft system were derived by computing the variation of Casimir function which was added to the Hamiltonian. The stable region of the parameter space was given and validated by numerical computation. Related results suggest that the change of inertia matrix, the length of flexible attachment, spacecraft spinning rate, and filled ratio of liquid fuel tank have strong influence on the stability of the spacecraft system.