dc.contributor.author |
Fontana-McNally, J. |
dc.contributor.author |
Miranda, E. |
dc.contributor.author |
Peralta-Salas, D. |
dc.date.accessioned |
2024-03-04T11:29:56Z |
dc.date.available |
2024-03-04T11:29:56Z |
dc.date.issued |
2024-01-31 |
dc.identifier.uri |
http://hdl.handle.net/2072/537458 |
dc.description.sponsorship |
J.F.-M. is supported by an UPC-INIREC grant through the grant ‘Computational, dynamical and geometrical complexity in fluid dynamics’, Ayudas Fundación BBVA a Proyectos de Investigación Científica 2021. J.F.-M. and E.M. are both partially supported by the Spanish State Research Agency grant no. PID2019-103849GB-I00 of AEI/10.13039/501100011033 and by the AGAUR project 2021 SGR 00603 Geometry of Manifolds and Applications, GEOMVAP. All the authors are partially supported by the grant ‘Computational, dynamical and geometrical complexity in fluid dynamics’, Ayudas Fundación BBVA a Proyectos de Investigación Científica 2021. E.M. is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2021 and by the Alexander Von Humboldt foundation via a Friedrich Wilhelm Bessel Research Award. E.M. is also supported by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (project CEX2020-001084-M). D.P.-S. is supported by the grant nos. CEX2019-000904-S, RED2022-134301-T and PID2022-136795NB-I00 funded by MCIN/AEI/10.13039/501100011033. |
dc.format.extent |
16 p. |
dc.language.iso |
eng |
dc.publisher |
Royal Society Publishing |
dc.relation.ispartof |
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
Beltrami vector field; Contact geometry; Euler equations; Lifted metric; Reeb vector field |
dc.title |
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/publishedVersion |
dc.embargo.terms |
cap |
dc.identifier.doi |
10.1098/rspa.2023.0499 |
dc.rights.accessLevel |
info:eu-repo/semantics/openAccess |
dc.description.abstract |
We prove that the correspondence between Reeb and Beltrami vector fields presented in Etnyre & Ghrist (Etnyre, Ghrist 2000 Nonlinearity 13, 441–458 (doi:10.1088/0951-7715/13/2/306)) can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that energy levels above the maximum of the potential energy of mechanical Hamiltonian systems can be viewed as stationary fluid flows, though the metric is not prescribed. In particular, we showcase the emblematic example of the n-body problem and focus on the Kepler problem. We explicitly construct a compatible Riemannian metric that makes the Kepler problem of celestial mechanics a stationary fluid flow (of Beltrami type) on a suitable manifold, the Kepler–Euler flow. ©2024 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |