NONRECURSIVE ORDER-N FORMULATION OF MULTIBODY DYNAMICS

Although excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degreees of freedom. Algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors. This paper addresses these problems by employing the range space formulation of multibody dynamics and solving for multipliers using the preconditioned conjugate gradient method. By employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the range space metric. The method can achieve performance rates that depend linearly on the number of substructures. Furthermore, the approach is promising as a potential parallel processing algorithm in that it exhibits fine parallel granularity, is nonassembling, and is easily load balanced among processors without relying an system topology to induce parallelism.