Topological Analysis of Multibody Systems for Recursive Dynamics Formulations

Abstract

Abstract Graph theory is used to characterize the topology of multibody systems for high speed parallel computer dynamic simulation. Decoupled loops are defined for use in the recursive dynamics formulations, wherein Langrange multipliers can be eliminated concurrently within each decoupled loop. A row-scanning process for the nondirected adjacency matrix of a graph is described, to generate an identification array that facilitates compact storage and defines system connectivities. A decision tree search algorithm is employed to generate all spanning trees associated with a closed loop graph. For each spanning tree generated from the decision tree search algorithm, a precedence array is defined. A path matrix for the spanning tree and an outdegree of junction nodes are defined to assist in parallel implementation of recursive dynamics algorithms and are then constructed from the precedence array. Finally, an optimal tree search algorithm that identifies a spanning tree that leads to best solution sequences for parallel implementation of recursive dynamics formulations is presented.