Abstract: According to the motion characteristics of flexible cable pendulum, the sling movement of crane vessel was decomposed into rope swing component and rope fluctuations component which are independent mutually. Using string vibration theory, this paper constructed a wire fluctuations mathematics model, which can ensure existence uniqueness under mixed initial boundary conditions. In addition, using unconditional stable hidden type difference method, it resolved the fluctuations equation numerical solutions stability. The life-like wire movement was  obtained by applying a hanging property swing mathematics model in which ball coordinates represent swing angle and the principle of superposition. The simulation results show that the mathematical model and the algorithm proposed in this paper can effectively solve the realistic sling real-time motion.

Key words: flexible cable pendulum, wave equation, implicit difference method, superposition principle