Dynamic analysis of spatial flexible multibody systems using joint co‐ordinates

This paper presents a systematic method for deriving the minimum number of equations of motion for spatial flexible multibody systems. Relative kinematics are developed using relative joint co‐ordinates and relative joint velocities to formulate a minimum number of equations of motion. The present method takes advantage of the simplicity of the absolute co‐ordinate formulation and computational efficiency of the relative joint co‐ordinate formulation. The system equations of motion are first formulated in terms of a coupled set of absolute reference co‐ordinates and elastic modal co‐ordinates. These equations are transformed to the joint co‐ordinate space by use of a velocity transformation matrix including the elastic modal velocities. A computer algorithm is proposed and extended to closed loop mechanisms. One example of a flexible vehicle is presented and the results are discussed to illustrate the computational efficiency of the method.