Open systems in classical mechanics

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https://doi.org/10.1063/5.0029885

Document Type

Research Article

Publication Title

Journal of Mathematical Physics

Publication Date

4-1-2021

doi

10.1063/5.0029885

Abstract

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

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