An algebraic approach to discrete mechanics
type: Item
instance of: scholarly article
title: An algebraic approach to discrete mechanics
zbMATH Open document ID: 0805.58031
DOI: 10.1007/BF00761712
author: John Baez
author: James W. Gilliam
published in: Letters in Mathematical Physics
publication date: 1994-07-18T00:00:00Z
review text: Using basic ideas of algebraic geometry the authors extend the methods of Lagrangian and symplectic mechanics to treat a large class of discrete mechanical systems, that is, systems such as cellular automata, in which time proceeds in integer steps and the configuration space is discrete. In particular, the authors derive an analog of the Euler-Lagrange equation from a variational principle, and prove an analog of Noether's theorem. The authors also construct a symplectic structure on the analog of the phase space and prove that it is preserved by time evolution.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 70H03
zbMATH DE Number: 606905
zbMATH Keywords: discrete mechanics
zbMATH Keywords: Noether's theorem
zbMATH Keywords: symplectic structure
reviewed by: Yoshihide Kozai
Wikidata QID: Q62443667
MaRDI profile type: Publication
cites work: Discrete Lagrange's equations and canonical equations based on the principle of least action
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cites work: p-adic dynamics
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full work available at URL: https://doi.org/10.1007/bf00761712
OpenAlex ID: W2132676772
description: scientific article; zbMATH DE number 606905