Extension of Delaunay normalisation for arbitrary powers of the radial distance

In the framework of perturbed Keplerian systems we deal with the Delaunay normalisation of a wide class of perturbations such that the radial distance is raised to an arbitrary real number ϒ. The averaged function is expressed in terms of the Gauss hypergeometric function 2F1 whereas the associated...

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Autores: Lanchares Sánchez, Ernesto, Palacián Subiela, Jesús Francisco
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/52543
Acceso en línea:https://hdl.handle.net/2454/52543
Access Level:acceso abierto
Palabra clave:Averaged Hamiltonian
Closed form expressions
Gauss and Appell hypergeometric functions
Generating function
Normalisation of Delaunay
Perturbed Keplerian Hamiltonians
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spelling Extension of Delaunay normalisation for arbitrary powers of the radial distanceLanchares Sánchez, ErnestoPalacián Subiela, Jesús FranciscoAveraged HamiltonianClosed form expressionsGauss and Appell hypergeometric functionsGenerating functionNormalisation of DelaunayPerturbed Keplerian HamiltoniansIn the framework of perturbed Keplerian systems we deal with the Delaunay normalisation of a wide class of perturbations such that the radial distance is raised to an arbitrary real number ϒ. The averaged function is expressed in terms of the Gauss hypergeometric function 2F1 whereas the associated generating function is the so called Appell hypergeometric function F1. The Gauss hypergeometric function related to the average depends on the eccentricity, e, whereas the Appell function depends additionally on the eccentric anomaly, E, and both special functions are properly defined and evaluated for all e Є [0,1) and E Є [-ꙥ ꙥ]. We analyse when the functions we determine can be extended to e=1. When the exponent of the radial distance is an integer, the usual values of the averaged and generating functions are recovered.The authors received partial support from Project PID2022-140469NB-C21 of the Ministry of Science, Innovation and Universities of Spain.ElsevierEstadística, Informática y MatemáticasEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT22025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/52543reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-140469NB-C21© 2024 The Authors. This is an open access article under the CC BY-NC license.https://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/525432026-06-17T12:41:47Z
dc.title.none.fl_str_mv Extension of Delaunay normalisation for arbitrary powers of the radial distance
title Extension of Delaunay normalisation for arbitrary powers of the radial distance
spellingShingle Extension of Delaunay normalisation for arbitrary powers of the radial distance
Lanchares Sánchez, Ernesto
Averaged Hamiltonian
Closed form expressions
Gauss and Appell hypergeometric functions
Generating function
Normalisation of Delaunay
Perturbed Keplerian Hamiltonians
title_short Extension of Delaunay normalisation for arbitrary powers of the radial distance
title_full Extension of Delaunay normalisation for arbitrary powers of the radial distance
title_fullStr Extension of Delaunay normalisation for arbitrary powers of the radial distance
title_full_unstemmed Extension of Delaunay normalisation for arbitrary powers of the radial distance
title_sort Extension of Delaunay normalisation for arbitrary powers of the radial distance
dc.creator.none.fl_str_mv Lanchares Sánchez, Ernesto
Palacián Subiela, Jesús Francisco
author Lanchares Sánchez, Ernesto
author_facet Lanchares Sánchez, Ernesto
Palacián Subiela, Jesús Francisco
author_role author
author2 Palacián Subiela, Jesús Francisco
author2_role author
dc.contributor.none.fl_str_mv Estadística, Informática y Matemáticas
Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
dc.subject.none.fl_str_mv Averaged Hamiltonian
Closed form expressions
Gauss and Appell hypergeometric functions
Generating function
Normalisation of Delaunay
Perturbed Keplerian Hamiltonians
topic Averaged Hamiltonian
Closed form expressions
Gauss and Appell hypergeometric functions
Generating function
Normalisation of Delaunay
Perturbed Keplerian Hamiltonians
description In the framework of perturbed Keplerian systems we deal with the Delaunay normalisation of a wide class of perturbations such that the radial distance is raised to an arbitrary real number ϒ. The averaged function is expressed in terms of the Gauss hypergeometric function 2F1 whereas the associated generating function is the so called Appell hypergeometric function F1. The Gauss hypergeometric function related to the average depends on the eccentricity, e, whereas the Appell function depends additionally on the eccentric anomaly, E, and both special functions are properly defined and evaluated for all e Є [0,1) and E Є [-ꙥ ꙥ]. We analyse when the functions we determine can be extended to e=1. When the exponent of the radial distance is an integer, the usual values of the averaged and generating functions are recovered.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/52543
url https://hdl.handle.net/2454/52543
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-140469NB-C21
dc.rights.none.fl_str_mv © 2024 The Authors. This is an open access article under the CC BY-NC license.
https://creativecommons.org/licenses/by-nc/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2024 The Authors. This is an open access article under the CC BY-NC license.
https://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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