Abstract: Any complex mechanical multibody system can be transformed into an equivalent tree system. Based on the spatial operator algebra theory, the recursive dynamics process for liquid-filled system is introduced considering small amplitude liquid sloshing, and the sloshing force between tank and liquid can be obtained by momentum theorem and the momentum moment theorem as the tank and liquid are regarded as individual bodies. The wave height function and velocity potential function expressed by modal variables are derived from the modal analysis theory of finite element method. The tank and its adjacent objects are connected with the equivalent spring and damping and by using an inboard 6-DOF virtual hinge attached on the reference frame of tank the kinematics and dynamic variables can be transferred and the maximum amount of information of liquid sloshing can be saved. The multibody system inboard joint of the tank is treated as an under-actuated joint in unknown tank movement circumstance, so as to derive the recursive dynamic algorithm for liquid-filled system under small amplitude liquid sloshing based on the spatial operator algebra theory which still holds on the rigid-liquid coupling mechani.

Key words: Liquid sloshing, Multibody system dynamics, Recursive algorithm, Spatial operator algebra