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 |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2020
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| 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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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. en 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.
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| 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 |
| _version_ |
1851756965462540288 |