This paper presents an extension of a newly developed multi-body system dynamics formulation to systems with general topology. The State-Time dynamic formulation, which has been recently developed by the authors, provides the means to yield significantly reduced simulation turnaround time through its ability to better exploit massively parallel computing resources. The rules provided in this article are useful in automating the generation of system 's equations of motion and in determining the final form of the system tangent matrix arising in this formulation. A priori knowledge of this structure assists one to find a proper ordering for the rows and columns of this matrix such that the final structure is optimized from data storage and solution expense perspectives. Also, the extended formulation enables one to eliminate the constraint forces or to bring only the desirable ones into evidence and as such results in a reduced set of equations and unknowns. Examples are provided to demonstrate application of the given rules.
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