Abstract: The dynamic model of a kind of boom crane mounted on ships is established. The relative kinetic energy is calculated in the non-inertial coordinate frame fixed on the crane ship. Introducing the inertial force, the Lagrange’s equations successfully depict the movement of the system consisting of the boom and payload, which is impacted not only by the control forces：the luffing and slewing moments of the boom and the rope’s strain, but also the 6 degrees of the crane ship’s movement mainly caused by ocean wave. The structure of the obtained model is suitable for the dynamics analysis and controller design for the system. Some kinematic features are demonstrated by the provided simulation result

Key words: Dynamics modeling, Ship-mounted crane, Underactuated system