Open Systems in Classical Mechanics

Abstract

Generalized span categories provide a framework for formalizing mathematical models of open systems in classical mechanics. We introduce categories $\mathsf{LagSy}$ and $\mathsf{HamSy}$ that respectively provide a categorical framework for the Lagrangian and Hamiltonian descriptions of open classical mechanical systems. The morphisms of $\mathsf{LagSy}$ and $\mathsf{HamSy}$ correspond to such open systems, and composition of morphisms models the construction of systems from subsystems. The Legendre transformation gives rise to a functor from $\mathsf{LagSy}$ to $\mathsf{HamSy}$ that translates from the Lagrangian to the Hamiltonian perspective.

31 pages

References in corpus (7)

• A Universal Construction for (Co)Relations
• A Compositional Framework for Reaction Networks
• Lecture Notes on Mathematical Methods of Classical Physics
• Open Systems: A Double Categorical Perspective
• An algebra of open continuous time dynamical systems and networks
• Structured Cospans
• Constructing Span Categories From Categories Without Pullbacks

Cited by in corpus (6)

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• Constructing Span Categories From Categories Without Pullbacks
• Organizing Physics with Open Energy-Driven Systems
• Singular Riemannian foliations and $\mathcal{I}$-Poisson manifolds