Improved 'Order-N' performance algorithm for the simulation of constrained multi-rigid-body dynamic systems

This paper presents an algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The algorithm can accommodate the spatial motion of general multi-rigid-body systems containing arbitrarily many closed loops in O(n + m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called 'O(n)' state-space formulations, when dealing with constraints which tend to actually show O(n + m + nm + nm(2) + m(3)) performance. Additionally, these latter formulations may require additional constraint violation stabilization procedures (e. g. Baumgarte's method, coordinate partitioning, etc.) which can contribute significant additional computation. The presented method suffers less from this difficulty because the loop closure constraints at both the velocity and acceleration level are directly embedded within the formulation. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and m.