A compositional framework for classical kinematic systems

TL;DR

This paper introduces a category-theoretic framework for classical kinematic systems that models open systems, handles geometric constraints, and clarifies subsystem interactions, providing a unified and precise mathematical description.

Contribution

It develops a novel categorical approach to describe open kinematic systems, including feedback and constraints, unifying various system types within a single formalism.

Findings

Framework models open systems as morphisms in a category

Supports precise treatment of geometric constraints

Clarifies interactions in lower kinematic pairs

Abstract

Our aim is to introduce a category-theoretic framework sufficiently general to describe a wide variety of open kinematic systems in classical mechanics while uniquely characterizing systems with specified simplest components. The framework models open systems as morphisms in a category $\mathsf{Kin}(\mathcal{F})$, where composition encodes relationships between subsystems and their embedding into larger systems. Unlike previous approaches, the framework supports a precise treatment of geometric constraints, enabling the characterization of systems with feedback. A consequence is a structural formulation of lower kinematic pairs that clarifies system interactions.