Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates

We consider superintegrability in classical mechanics in the presence of magnetic fields. We focus on three-dimensional systems that are separable in Cartesian coordinates. We construct all possible minimally and maximally superintegrable systems in this class with additional integrals quadratic in...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2020
Hauptverfasser: Marchesiello, Antonella, Šnobl, Libor
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/210595
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Zitieren:Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates. Antonella Marchesiello and Libor Šnobl. SIGMA 16 (2020), 015, 35 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-210595
record_format dspace
spelling Marchesiello, Antonella
Šnobl, Libor
2025-12-12T10:35:47Z
2020
Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates. Antonella Marchesiello and Libor Šnobl. SIGMA 16 (2020), 015, 35 pages
1815-0659
2020 Mathematics Subject Classification: 37J35; 78A25
arXiv:1911.01180
https://nasplib.isofts.kiev.ua/handle/123456789/210595
https://doi.org/10.3842/SIGMA.2020.015
We consider superintegrability in classical mechanics in the presence of magnetic fields. We focus on three-dimensional systems that are separable in Cartesian coordinates. We construct all possible minimally and maximally superintegrable systems in this class with additional integrals quadratic in the momenta. Together with the results of our previous paper [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages], where one of the additional integrals was by assumption linear, we conclude the classification of three-dimensional quadratically minimally and maximally superintegrable systems separable in Cartesian coordinates. We also describe two particular methods for constructing superintegrable systems with higher-order integrals.
This paper was supported by the Czech Science Foundation (Grant Agency of the Czech Republic), project 17-11805S. This paper is dedicated to our son Flavio, born just after the submission of the original manuscript.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates
spellingShingle Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates
Marchesiello, Antonella
Šnobl, Libor
title_short Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates
title_full Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates
title_fullStr Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates
title_full_unstemmed Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates
title_sort classical superintegrable systems in a magnetic field that separate in cartesian coordinates
author Marchesiello, Antonella
Šnobl, Libor
author_facet Marchesiello, Antonella
Šnobl, Libor
publishDate 2020
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We consider superintegrability in classical mechanics in the presence of magnetic fields. We focus on three-dimensional systems that are separable in Cartesian coordinates. We construct all possible minimally and maximally superintegrable systems in this class with additional integrals quadratic in the momenta. Together with the results of our previous paper [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages], where one of the additional integrals was by assumption linear, we conclude the classification of three-dimensional quadratically minimally and maximally superintegrable systems separable in Cartesian coordinates. We also describe two particular methods for constructing superintegrable systems with higher-order integrals.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210595
citation_txt Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates. Antonella Marchesiello and Libor Šnobl. SIGMA 16 (2020), 015, 35 pages
work_keys_str_mv AT marchesielloantonella classicalsuperintegrablesystemsinamagneticfieldthatseparateincartesiancoordinates
AT snobllibor classicalsuperintegrablesystemsinamagneticfieldthatseparateincartesiancoordinates
first_indexed 2025-12-17T12:04:18Z
last_indexed 2025-12-17T12:04:18Z
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