The linear symmetries of Hill’s lunar problem

A symmetry of a Hamiltonian system is a symplectic or anti-symplectic involution which leaves the Hamiltonian invariant. For the planar and spatial Hill lunar problem, four resp. eight linear symmetries are well-known. Algebraically, the planar ones form a Klein four-group [Formula: see text] and th...

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Autor principal: Aydin, Cengiz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9938827/
https://www.ncbi.nlm.nih.gov/pubmed/36814433
http://dx.doi.org/10.1007/s00013-022-01822-1
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author Aydin, Cengiz
author_facet Aydin, Cengiz
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description A symmetry of a Hamiltonian system is a symplectic or anti-symplectic involution which leaves the Hamiltonian invariant. For the planar and spatial Hill lunar problem, four resp. eight linear symmetries are well-known. Algebraically, the planar ones form a Klein four-group [Formula: see text] and the spatial ones form the group [Formula: see text] . We prove that there are no other linear symmetries. Remarkably, in Hill’s system the spatial linear symmetries determine already the planar linear symmetries.
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spelling pubmed-99388272023-02-20 The linear symmetries of Hill’s lunar problem Aydin, Cengiz Arch Math Article A symmetry of a Hamiltonian system is a symplectic or anti-symplectic involution which leaves the Hamiltonian invariant. For the planar and spatial Hill lunar problem, four resp. eight linear symmetries are well-known. Algebraically, the planar ones form a Klein four-group [Formula: see text] and the spatial ones form the group [Formula: see text] . We prove that there are no other linear symmetries. Remarkably, in Hill’s system the spatial linear symmetries determine already the planar linear symmetries. Springer International Publishing 2023-01-16 2023 /pmc/articles/PMC9938827/ /pubmed/36814433 http://dx.doi.org/10.1007/s00013-022-01822-1 Text en © The Author(s) 2023 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/) .
spellingShingle Article
Aydin, Cengiz
The linear symmetries of Hill’s lunar problem
title The linear symmetries of Hill’s lunar problem
title_full The linear symmetries of Hill’s lunar problem
title_fullStr The linear symmetries of Hill’s lunar problem
title_full_unstemmed The linear symmetries of Hill’s lunar problem
title_short The linear symmetries of Hill’s lunar problem
title_sort linear symmetries of hill’s lunar problem
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9938827/
https://www.ncbi.nlm.nih.gov/pubmed/36814433
http://dx.doi.org/10.1007/s00013-022-01822-1
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