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Geometric and physical interpretation of the action principle
We give a geometric interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively “counts” the possible evolutions that “go through” the area enclosed. If the path corresponds t...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10372048/ https://www.ncbi.nlm.nih.gov/pubmed/37495640 http://dx.doi.org/10.1038/s41598-023-39145-y |
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author | Carcassi, Gabriele Aidala, Christine A. |
author_facet | Carcassi, Gabriele Aidala, Christine A. |
author_sort | Carcassi, Gabriele |
collection | PubMed |
description | We give a geometric interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively “counts” the possible evolutions that “go through” the area enclosed. If the path corresponds to a possible evolution, all neighbouring evolutions will be parallel, making them tangent to the area enclosed by the path and its variation, thus yielding a stationary action. This treatment gives a full physical account of the geometry of both Hamiltonian and Lagrangian mechanics which is founded on three assumptions: determinism and reversible evolution, independence of the degrees of freedom and equivalence between kinematics and dynamics. The logical equivalence between the three assumptions and the principle of stationary action leads to a much cleaner conceptual understanding. |
format | Online Article Text |
id | pubmed-10372048 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-103720482023-07-28 Geometric and physical interpretation of the action principle Carcassi, Gabriele Aidala, Christine A. Sci Rep Article We give a geometric interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively “counts” the possible evolutions that “go through” the area enclosed. If the path corresponds to a possible evolution, all neighbouring evolutions will be parallel, making them tangent to the area enclosed by the path and its variation, thus yielding a stationary action. This treatment gives a full physical account of the geometry of both Hamiltonian and Lagrangian mechanics which is founded on three assumptions: determinism and reversible evolution, independence of the degrees of freedom and equivalence between kinematics and dynamics. The logical equivalence between the three assumptions and the principle of stationary action leads to a much cleaner conceptual understanding. Nature Publishing Group UK 2023-07-26 /pmc/articles/PMC10372048/ /pubmed/37495640 http://dx.doi.org/10.1038/s41598-023-39145-y Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Carcassi, Gabriele Aidala, Christine A. Geometric and physical interpretation of the action principle |
title | Geometric and physical interpretation of the action principle |
title_full | Geometric and physical interpretation of the action principle |
title_fullStr | Geometric and physical interpretation of the action principle |
title_full_unstemmed | Geometric and physical interpretation of the action principle |
title_short | Geometric and physical interpretation of the action principle |
title_sort | geometric and physical interpretation of the action principle |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10372048/ https://www.ncbi.nlm.nih.gov/pubmed/37495640 http://dx.doi.org/10.1038/s41598-023-39145-y |
work_keys_str_mv | AT carcassigabriele geometricandphysicalinterpretationoftheactionprinciple AT aidalachristinea geometricandphysicalinterpretationoftheactionprinciple |