Improved `Order-N' Performance Algorithm for the Simulation of Constrained Multi-Rigid-Body Dynamic Systems

This paper presents an algorithm for the efficient numerical analysisand simulation of modest to heavily constrained multi-rigid-body dynamicsystems. The algorithm can accommodate the spatial motion of generalmulti-rigid-body systems containing arbitrarily many closed loops inO(n + m)operations overall for systems containing n generalizedcoordinates, and m independent algebraic constraints. The presentedapproach does not suffer from the performance (speed) penaltyencountered by most other of the so-called `O(n)' state-spaceformulations, when dealing with constraints which tend to actually showO(n + m + nm + nm2+ m3) performance. Additionally, these latterformulations may require additional constraint violation stabilizationprocedures (e.g. Baumgarte's method, coordinate partitioning, etc.)which can contribute significant additional computation. The presentedmethod suffers less from this difficulty because the loop closureconstraints at both the velocity and acceleration level are directlyembedded within the formulation. Due to these characteristics, thepresented algorithm offers superior computing performance relative toother methods in situations involving both large n and m.