Abstract: A relative coordinate svstem is presented to describe the motion of multi-body systems.This coordinate system fully utilizes the property of translation matrix,sothat the nonlinear couplings between rigid motion and elastic motion are greatly reduced. The equations of planar and spatial deformable body are derived based on finite elemeiitmethod and Lagrange' s equation. Numerical methods for solving the equations are alsodiscussed and the generalized coordinate partitioning method is presented.According tot...