This paper presents an addendum to the Recursive Coordinate Reduction (RCR) algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The RCR algorithm can accommodate the spatial motion of broad categories of 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 “(n)” state-space formulations, and does not require additional constraint violation stabilization procedures (e.g. Baumgartes method, coordinate partitioning, etc.). Due to these characteristics, the presented algorithm should offer superior computing performance relative to other methods in many situations involving both large n and m. This paper will specifically address an unpublished recursive step in the handling of “floating” loop base bodies, as well as present an extension to “spur” topologies.

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