A state-space dynamical representation for multibody mechanical systems part I: Systems with tree configuration

Abstract

The dynamical equations of motion of a multibody system with closed loops are reduced to state space equations within the framework of the computer-oriented Roberson/Wittenburg multibody formalism. First, that formalism is reviewed. One obtains unreduced equations of motion for systems with tree configuration as well as systems with closed loops. The constraint equations are discussed next, formulated in terms of variables representing the relative motion of contiguous interacting bodies. For systems with tree configurations, such constraint equations can be used without further modification to reduce the dynamical equations to state space form, by applying methods of linear algebra. Modes of motion are derived from the constraints and the interaction forces and torques between the bodies are separated into generalized applied and constraint forces. The latter are eliminated, thus reducing the dynamical equations to state space form. Finally, the relations for the determination of the generalized constraint forces are given, assuming that the motion of the system has been determined from its state space representation.