ON THE USE OF LINEAR GRAPH-THEORY IN MULTIBODY SYSTEM DYNAMICS

Multibody dynamics involves the generation and solution of the equatio ns of motion for a system of connected material bodies. The subject of this paper is the use of graph-theoretical methods to represent multi body system topologies and to formulate the desired set of motion equa tions; a discussion of the methods available for solving these differe ntial-algebraic equations is beyond the scope of this work. After a br ief introduction to the topic, a review of linear graphs and their ass ociated topological arrays is presented, followed in turn by the use o f these matrices in generating various graph-theoretic equations. The appearance of linear graph theory in a number of existing multibody fo rmulations is then discussed, distinguishing between approaches that u se absolute (Cartesian) coordinates and those that employ relative (jo int) coordinates. These formulations are then contrasted with formal g raph-theoretic approaches, in which both the kinematic and dynamic equ ations are automatically generated from a single linear graph represen tation of the system. The paper concludes with a summary of results an d suggestions for further research on the graph-theoretical modelling of mechanical systems.