Contemporary problem formulation methods used in the dynamic simulation of rigid bodies suffer from problems in accuracy, performance, and robustness. Significant allowances for parameter tuning, coupled with careful implementation of a broad-phase collision detection scheme are required to make dynamic simulation useful for practical applications. A constraint formulation method is presented herein that is more robust, and not dependent on broad-phase collision detection or system tuning for its behavior. Several uncomplicated benchmark examples are presented to give an analysis and make a comparison of the new polyhedral exact geometry (PEG) method with the well-known Stewart–Trinkle method. The behavior and performance for the two methods are discussed. This includes specific cases where contemporary methods fail to match theorized and observed system states in simulation, and how they are ameliorated by the new method presented here. The goal of this work is to complete the groundwork for further research into high performance simulation.