Recursive formulations of a flexible multibody system by the method of weighted residual

This paper deals with recursive formulations of flexible bodies connected by rotary joints based on the method of weighted residual. As the state variables, the translational velocity of the base body, the angular velocities of the bodies, and the modal amplitudes of elastic deformation of the bodies are employed. Using two sets of weighted functions, two types of mathematical models of the system are obtained in recursive forms; The first one is an extension of the model of a rigid multibody system based on the Newton-Euler's method. The second one is the same as the model based on the Lagrangian formulation with quasi coordinates. The recursive algorithms of the inverse dynamics of a flexible manipulator are derived using the models obtained.