A compositional framework for open classical kinematic systems
Abstract
Our aim is to introduce a framework sufficiently general to describe the kinematics of a wide variety of open systems in classical mechanics while uniquely characterizing systems with specified simplest components. The data describing a physical system are local, so the construction of a global configuration space requires compatibility among local interactions. We model open systems as morphisms in a category Kin(F), where composition encodes how subsystems attach to one another and embed into larger systems. The framework supports a precise treatment of geometric constraints and clarifies when locally specified subsystems are compatible. It also yields a structural approach to the study of linkages: we prove the nonconstructibility of sliding hinges and universal joints from two rigid bodies attached by a surface constraint compatible with rigid-motion symmetries.