Open systems in classical mechanics
| Autor: | David Weisbart, Adam Yassine, John C. Baez |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Span (category theory)
math-ph Mathematics::General Topology FOS: Physical sciences 18B10 01 natural sciences Mathematical Sciences 18B10 70A05 53Z05 Legendre transformation symbols.namesake math.MP Morphism Mathematics::Probability Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Mathematics::Metric Geometry Category Theory (math.CT) 0101 mathematics math.CT Categorical variable Mathematical Physics Mathematics Functor Mathematical model 010102 general mathematics 70A05 Mathematics - Category Theory 53Z05 Statistical and Nonlinear Physics Mathematical Physics (math-ph) Mechanical system Mathematics::Logic Classical mechanics Physical Sciences symbols 010307 mathematical physics Hamiltonian (control theory) |
| Zdroj: | Journal of Mathematical Physics, vol 62, iss 4 JOURNAL OF MATHEMATICAL PHYSICS, vol 62, iss 4 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/5.0029885 |
| Popis: | 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. Comment: 31 pages |
| Databáze: | OpenAIRE |
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