A Symbolic Formulation for Linearization of Multibody Equations of Motion

Abstract

This paper presents a method for obtaining linearized state space representations of open or closed loop multibody dynamic systems. The paper develops a symbolic formulation for multibody dynamic systems which result in an explicit set of symbolic equations of motion. The symbolic equations are then used to perform symbolic linearizations. The resulting symbolic, linear equations are in terms of the system parameters and the equilibrium point, and are valid for any equilibrium point. Finally, a method is developed for reducing a linearized, constrained multibody system consisting of a mixed set of algebraic-differential equations to a reduced set of differential equations in terms of an independent coordinate set. An example is used to demonstrate the technique.