AN ORDER-N FORMULATION FOR THE MOTION SIMULATION OF GENERAL MULTI-RIGID-BODY CONSTRAINED SYSTEMS

This paper presents a computer-based method for the efficient formulation and solution of the nonlinear equations of motion for mechanical systems, which are modeled as systems of interconnected rigid bodies and are subject to motion and/or geometric constraints. The procedure forms the equations of motion and solves for the system state derivatives associated with the unconstrained system in a highly efficient, order n manner. The constraint loads required to enforce the constraint relations are then determined through the use of a constraint stabilization method. The required constraint loads are then used to modify the state derivatives found previously, resulting in a set of state derivatives which are now associated with that of the constrained system. This procedure determines these state derivative values associated with the constrained system in effectively order n operations overall, while being immune to many of the problems associated with penalty procedures and other constraint stabilization strategies.