Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold
In this paper we aim at presenting a concise but also comprehensive study of time-dependent (<i>t</i>-dependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations in order to formulate an explicit...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/4/843 |
| _version_ | 1797603446582411264 |
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| author | Marcin Zając Cristina Sardón Orlando Ragnisco |
| author_facet | Marcin Zając Cristina Sardón Orlando Ragnisco |
| author_sort | Marcin Zając |
| collection | DOAJ |
| description | In this paper we aim at presenting a concise but also comprehensive study of time-dependent (<i>t</i>-dependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations in order to formulate an explicitly time-dependent geometric Hamilton-Jacobi theory on lcs manifolds, extending our previous work with no explicit time-dependence. In contrast to previous papers concerning locally conformal symplectic manifolds, the introduction of the time dependency that this paper presents, brings out interesting geometric properties, as it is the case of contact geometry in locally symplectic patches. To conclude, we show examples of the applications of our formalism, in particular, we present systems of differential equations with time-dependent parameters, which admit different physical interpretations as we shall point out. |
| first_indexed | 2024-03-11T04:29:19Z |
| format | Article |
| id | doaj.art-a1eb2a89b5544c5a8bec0bb501b45da5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T04:29:19Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a1eb2a89b5544c5a8bec0bb501b45da52023-11-17T21:33:30ZengMDPI AGSymmetry2073-89942023-04-0115484310.3390/sym15040843Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic ManifoldMarcin Zając0Cristina Sardón1Orlando Ragnisco2Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, PolandDepartment of Applied Mathematics, Universidad Politécnica de Madrid, 28006 Madrid, SpainDepartment of Mathematics and Physics, University degli Studi Roma Tre, 00146 Rome, ItalyIn this paper we aim at presenting a concise but also comprehensive study of time-dependent (<i>t</i>-dependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations in order to formulate an explicitly time-dependent geometric Hamilton-Jacobi theory on lcs manifolds, extending our previous work with no explicit time-dependence. In contrast to previous papers concerning locally conformal symplectic manifolds, the introduction of the time dependency that this paper presents, brings out interesting geometric properties, as it is the case of contact geometry in locally symplectic patches. To conclude, we show examples of the applications of our formalism, in particular, we present systems of differential equations with time-dependent parameters, which admit different physical interpretations as we shall point out.https://www.mdpi.com/2073-8994/15/4/843canonical transformationstime-dependent hamiltonian dynamicslocally conformal symplectictime-dependent Hamilton Jacobi |
| spellingShingle | Marcin Zając Cristina Sardón Orlando Ragnisco Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold Symmetry canonical transformations time-dependent hamiltonian dynamics locally conformal symplectic time-dependent Hamilton Jacobi |
| title | Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold |
| title_full | Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold |
| title_fullStr | Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold |
| title_full_unstemmed | Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold |
| title_short | Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold |
| title_sort | time dependent hamiltonian mechanics on a locally conformal symplectic manifold |
| topic | canonical transformations time-dependent hamiltonian dynamics locally conformal symplectic time-dependent Hamilton Jacobi |
| url | https://www.mdpi.com/2073-8994/15/4/843 |
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