Mathematical modeling of a slewing crane mechanism with moving payload pendulum

A slewing crane which is handling payload via rotation and. moving the carriage simultaneously can be modeled as a system consisting of a rotary flexible clamed-free beam with the spherical payload pendulum that moves along the beam. This work completes the mathematical modeling of such system. Euler-Bemoulli beam theory has been used to model the clamed-free beam attached to a rotating hub. The payload is modeled as a sphere pendulum of point mass attached to carriage via mass less inextensible cable. The carriage can move on the rotating beam. The Hamilton principle has been used to derive nonlinear coupled equations of motion of the in-plane and out-of-plane of the beam and the payload pendulum. Some remarks are made on the equations of motion.