A Systematic Formulation for Dynamics of Flexible Multi-Body Systems Using the Velocity Transformation Technique

Abstract

An efficient and systematic formulation for dynamics of spatial multi-body systems with flexible bodies is presented using the velocity transformation technique. The Cartesian variables are expressed in terms of the relative and elastic variables. Using the resulting kinemtic relationships, the velocity and acceleration transformation equations are derived and used to transform the equations of motion from the Cartesian coordinate space to the relative coordinate space. In order to reduce the number of elastic coordinates, elastic deformations are represented by the vibration normal modes obtained from the finite element analysis. The Euler parameters are used as the rotational coordinates since they are convenient for algebraic manipulation and have no singular condition. The formulation is illustrated by means of two numerical examples.