Constructive collisions

Abstract

This paper studies the semantics of models for discrete physical phenomena such as rigid body collisions. The paper combines generalized functions (specifically the Dirac delta function), superdense time, modal models, and constructive semantics to get a rich, flexible, efficient, and rigorous approach to modeling such systems. It shows that many physical scenarios that have been problematic formodeling techniquesmanifest as nonconstructive models, and that constructive versions of some of the models properly reflect uncertainty in the behavior of the physical systems that plausibly arise from the principles of quantum mechanics. The paper argues that these modeling difficulties are not reasonably solved by more detailed continuous models of the underlying physical phenomena. Such more detailed models simply shift the uncertainty to other aspects of the model. Since such detailed models come with a high computational cost, there is little justification in using them unless the goal of modeling is specifically to understand these more detailed physical processes. An implementation of these methods in the Ptolemy II modeling and simulation environment is described. © 2014 Springer-Verlag Berlin Heidelberg.