Wittenburg's formulation of multibody dynamics equations from a graph-theoretic perspective

Abstract

In the past 20 years, many multibody or “self-formulating” computer programs have been developed for the simulation of dynamic mechanical systems. These programs are based on algorithms that enable the computer to formulate, automatically, the equations of motion for a specified system, given only a description of the system as input; numerical methods can be applied to the resulting differential-algebraic equations in order to determine the time response of the system. Whether explicitly or implicitly, all of these multibody algorithms use concepts from linear graph theory in some form or another. The “vector-network technique” represents a direct application of graph-theoretic methods to dynamic mechanical systems. In contrast, Wittenburg's well-known formalism for creating the equations of motion appears, at first glance, to use linear graph theory for the sole purpose of representing the system topology. The goal of this paper is to examine in detail the relationship between these two methodologies. In particular, the authors will establish the equivalence of the equations derived using Wittenburg's formulation, and those arising out of a formal graph-theoretic approach.