Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tensor, hereafter called a concircular tensor. First, w...
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| Дата: | 2016 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148531 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature / K. Rajaratnam, R.G. McLenaghan, C. Valero // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1485312019-02-19T01:24:09Z Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature Rajaratnam, K. McLenaghan, R.G. Valero, C. We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tensor, hereafter called a concircular tensor. First, we show how to extend original results given by Benenti to intrinsically characterize all (orthogonal) separable coordinates in spaces of constant curvature using concircular tensors. This results in the construction of a special class of separable coordinates known as Kalnins-Eisenhart-Miller coordinates. Then we present the Benenti-Eisenhart-Kalnins-Miller separation algorithm, which uses concircular tensors to intrinsically search for Kalnins-Eisenhart-Miller coordinates which separate a given natural Hamilton-Jacobi equation. As a new application of the theory, we show how to obtain the separable coordinate systems in the two dimensional spaces of constant curvature, Minkowski and (Anti-)de Sitter space. We also apply the Benenti-Eisenhart-Kalnins-Miller separation algorithm to study the separability of the three dimensional Calogero-Moser and Morosi-Tondo systems. 2016 Article Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature / K. Rajaratnam, R.G. McLenaghan, C. Valero // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C15; 70H20; 53A60 DOI:10.3842/SIGMA.2016.117 http://dspace.nbuv.gov.ua/handle/123456789/148531 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tensor, hereafter called a concircular tensor. First, we show how to extend original results given by Benenti to intrinsically characterize all (orthogonal) separable coordinates in spaces of constant curvature using concircular tensors. This results in the construction of a special class of separable coordinates known as Kalnins-Eisenhart-Miller coordinates. Then we present the Benenti-Eisenhart-Kalnins-Miller separation algorithm, which uses concircular tensors to intrinsically search for Kalnins-Eisenhart-Miller coordinates which separate a given natural Hamilton-Jacobi equation. As a new application of the theory, we show how to obtain the separable coordinate systems in the two dimensional spaces of constant curvature, Minkowski and (Anti-)de Sitter space. We also apply the Benenti-Eisenhart-Kalnins-Miller separation algorithm to study the separability of the three dimensional Calogero-Moser and Morosi-Tondo systems. |
| format |
Article |
| author |
Rajaratnam, K. McLenaghan, R.G. Valero, C. |
| spellingShingle |
Rajaratnam, K. McLenaghan, R.G. Valero, C. Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Rajaratnam, K. McLenaghan, R.G. Valero, C. |
| author_sort |
Rajaratnam, K. |
| title |
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature |
| title_short |
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature |
| title_full |
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature |
| title_fullStr |
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature |
| title_full_unstemmed |
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature |
| title_sort |
orthogonal separation of the hamilton-jacobi equation on spaces of constant curvature |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148531 |
| citation_txt |
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature / K. Rajaratnam, R.G. McLenaghan, C. Valero // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 41 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:29:42Z |
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