Helmoltz problem for the Riccati equation from an analogous Friedmann equation

We report a solution of the inverse Lagrangian problem for the first order Riccati differential equation by means of an analogy with the Friedmann equation of a suitable Friedmann–Lemaître–Robertson–Walker universe in general relativity. This analogous universe has fine-tuned parameters and is unphy...

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Autor principal: Faraoni, Valerio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Regular Article - Theoretical Physics
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8741700/
https://www.ncbi.nlm.nih.gov/pubmed/35069004
http://dx.doi.org/10.1140/epjc/s10052-021-09966-0
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author Faraoni, Valerio
author_facet Faraoni, Valerio
author_sort Faraoni, Valerio
collection PubMed
description We report a solution of the inverse Lagrangian problem for the first order Riccati differential equation by means of an analogy with the Friedmann equation of a suitable Friedmann–Lemaître–Robertson–Walker universe in general relativity. This analogous universe has fine-tuned parameters and is unphysical, but it suggests a Lagrangian and a Hamiltonian for the Riccati equation and for the many physical systems described by it.
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spelling pubmed-87417002022-01-20 Helmoltz problem for the Riccati equation from an analogous Friedmann equation Faraoni, Valerio Eur Phys J C Part Fields Regular Article - Theoretical Physics We report a solution of the inverse Lagrangian problem for the first order Riccati differential equation by means of an analogy with the Friedmann equation of a suitable Friedmann–Lemaître–Robertson–Walker universe in general relativity. This analogous universe has fine-tuned parameters and is unphysical, but it suggests a Lagrangian and a Hamiltonian for the Riccati equation and for the many physical systems described by it. Springer Berlin Heidelberg 2022-01-07 2022 /pmc/articles/PMC8741700/ /pubmed/35069004 http://dx.doi.org/10.1140/epjc/s10052-021-09966-0 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis 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/) . Funded by SCOAP3
spellingShingle Regular Article - Theoretical Physics
Faraoni, Valerio
Helmoltz problem for the Riccati equation from an analogous Friedmann equation
title Helmoltz problem for the Riccati equation from an analogous Friedmann equation
title_full Helmoltz problem for the Riccati equation from an analogous Friedmann equation
title_fullStr Helmoltz problem for the Riccati equation from an analogous Friedmann equation
title_full_unstemmed Helmoltz problem for the Riccati equation from an analogous Friedmann equation
title_short Helmoltz problem for the Riccati equation from an analogous Friedmann equation
title_sort helmoltz problem for the riccati equation from an analogous friedmann equation
topic Regular Article - Theoretical Physics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8741700/
https://www.ncbi.nlm.nih.gov/pubmed/35069004
http://dx.doi.org/10.1140/epjc/s10052-021-09966-0
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