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arXiv · 2602.20125

A compositional framework for open classical kinematic systems

Andrea Abeje-Stine·David Weisbart
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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 $\mathsf{Kin}(\mathcal{F})$, 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.

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Andrea Abeje-Stine, David Weisbart. 2026-02-23. A compositional framework for open classical kinematic systems. https://arxiv.org/abs/2602.20125

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