Dynamic Analysis of the Flexible Spacecraft with Liquid Sloshing in Axisymmetrical Container

In this paper, the modeling and dynamic analysis of the spacecraft carrying a flexible appendage and a partially fuel-filled arbitrary axisymmetrical tank with curved wall are investigated. Governing equations of the liquid sloshing in the container are derived from the variational principle. The dynamic equations of modal coordinates of the liquid sloshing are established by the Galerkin method. The coupling vibration equations of the flexible appendage are drawn from the theory of the Euler–Bernoulli beam. The state equations of coupled motion of the main rigid platform are deduced by using Lagrange’s equations in term of general quasi coordinates. Numerical results are presented to verify the efficiency and validity of the method developed in this paper. Related results suggest that there are complex dynamical behaviors in the flex–rigid–liquid coupling spacecraft dynamical systems, which have a reference value to the overall design of the spacecraft system.