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arXiv · 1710.11392

Open Systems in Classical Mechanics

John C. Baez·David Weisbart·Adam M. Yassine
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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.

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John C. Baez, David Weisbart, Adam M. Yassine. 2017-10-31. Open Systems in Classical Mechanics. https://doi.org/10.1063/5.0029885

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