Automated Procedures for Robust and Efficient Solution of Over-Constrained Multibody Dynamics

The basic steps of a computer-based methodology that generates optimized runtime algorithms to achieve robust, stable, and efficient solution of constrained, multibody dynamics are summarized. The concept of using processors operating in the background to improve many aspects of an executing program’s performance on arbitrary models is introduced. Among the many optimizing tasks, algorithm processors extract model topology from body and joint descriptions, set up recursive spatial kinematics and generalized dynamics algorithms, block-partition constraints and apply Gaussian elimination with complete pivoting to identify and change dependent and independent variable sets, convert constraints into row-reduced, echelon form, permute the constrained generalized equations to achieve stable and efficient solutions, and set up recursive sparse uncoupling and solve algorithms to minimize fills and operations count. To accomplish these tasks, processors assess model-specific algorithm requirements and use this information to generate source and destination memory pointer arrays and arrays of pointers to structures and optimized functions. In essence, they wire and rewire runtime algorithms as needed to maintain robust, stable, and efficient solutions throughout a simulation.