Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric
We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, fo...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/710274 |
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| _version_ | 1832567666893651968 |
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| author | Linyu Peng Huafei Sun Xiao Sun |
| author_facet | Linyu Peng Huafei Sun Xiao Sun |
| author_sort | Linyu Peng |
| collection | DOAJ |
| description | We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study
the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the
Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures,
the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, an N degrees of freedom linear Hamiltonian system and the Hénon-Heiles
model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model
are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads. |
| format | Article |
| id | doaj-art-9cbf5d6f988c43b28a690c18236d0764 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9cbf5d6f988c43b28a690c18236d07642025-02-03T01:00:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/710274710274Geometry of Hamiltonian Dynamics with Conformal Eisenhart MetricLinyu Peng0Huafei Sun1Xiao Sun2Department of Mathematics, University of Surrey, Guildford GU2 7XH, UKDepartment of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Automation, Beijing Institute of Technology, Beijing 100081, ChinaWe characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, an N degrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads.http://dx.doi.org/10.1155/2011/710274 |
| spellingShingle | Linyu Peng Huafei Sun Xiao Sun Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric International Journal of Mathematics and Mathematical Sciences |
| title | Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric |
| title_full | Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric |
| title_fullStr | Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric |
| title_full_unstemmed | Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric |
| title_short | Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric |
| title_sort | geometry of hamiltonian dynamics with conformal eisenhart metric |
| url | http://dx.doi.org/10.1155/2011/710274 |
| work_keys_str_mv | AT linyupeng geometryofhamiltoniandynamicswithconformaleisenhartmetric AT huafeisun geometryofhamiltoniandynamicswithconformaleisenhartmetric AT xiaosun geometryofhamiltoniandynamicswithconformaleisenhartmetric |