SOLUTION METHODS FOR DIFFERENTIAL ALGEBRAIC EQUATIONS IN MECHANICAL SYSTEMS SIMULATION

MECHANICAL SYSTEM SIMULATION (MSS) IS THE TECHNOLOGY USED TO ANALYZE SYSTEMS UNDERGOING LARGE OVERALL MOTION, SUCH AS AN AUTOMOBILE GOING OVER A POTHOLE OR A SPACE SHUTTLE PERFORMING SATELLITE RETRIEVAL. MSS FORMULATIONS LEAD TO A COUPLED SET OF DIFFERENTIAL AND ALGEBRAIC EQUATIONS CALLED INDEX-3 DAE. INDEX REDUCTION METHODS (IRM) ARE EMPLOYED TO SIMPLIFY AND SOLVE THESE EQUATIONS. THREE FACTORS DETERMINE THE ACCURACY AND STABILITY OF SOLUTIONS FOR MECHANICAL SYSTEMS: (1) THE SYSTEM STATES SELECTED, (2) THE IRM USED, AND (3) THE NUMERICAL INTEGRATOR USED. IDEALLY, THESE SELECTIONS SHOULD BE PROBLEM DRIVEN. YET, MOST COMMERCIAL MSS SOFTWARE APPLY VERY LIMITED COMBINATIONS OF THE ABOVE TO ALL PROBLEMS. THIS LIMITATION IS BEING ADDRESSED BY DEVELOPING A LIBRARY OF IRM AND INTEGRATORS, AND ALLOWING FOR THEIR INDEPENDENT SELECTION. RESEARCHERS ARE ENHANCING AN AUGMENTED LAGRANGIAN FORMULATION, AN IRM, TO CONTROL CONSTRAINT VIOLATION (ALF-CC), IMPLEMENT IT, AND DEMONSTRATE ITS EFFECTIVENESS WITH TWO INTEGRATORS. ALF-CC IS VERY ACCURATE AND FAST AND PROMISES TO SOLVE THROUGH SINGULAR CONFIGURATIONS, ACCOMMODATE INEQUALITY CONSTRAINTS, AND SYSTEM TOPOLOGY CHANGES. ALF-CC IS BEING COMPARED TO OTHER METHODS.