Compatibility and modeling of constrained dynamic systems

This paper deals with some fundamental problems of the constrained dynamic system, especially where dynamics and constraint are not congruous. First, we introduce a concept of compatibility of the system dynamics and constraint. It divides all constrained systems into three classes: incompatible (0% compatible), (partially) compatible, and congruous (100% compatible). We argue convincingly that the partially compatible case should be the focus of research. Second, we present useful conditions by which the compatibility of the general and a variety of constrained systems can be judged. Third, based on a careful examination of the partially compatible case, we propose several promising modeling strategies for two general situations: the dynamics given is in error and error free, respectively. In addition, we demonstrate that for the partially compatible case direct application of many existing results are flawed.