Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates
Recently we proposed a generic construction of the additional integrals of motion for the Stäckel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for elliptic and parabolic coordinate systems on the plane.
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2012-05-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.031 |
| _version_ | 1811259947246157824 |
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| author | Andrey V. Tsiganov |
| author_facet | Andrey V. Tsiganov |
| author_sort | Andrey V. Tsiganov |
| collection | DOAJ |
| description | Recently we proposed a generic construction of the additional integrals of motion for the Stäckel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for elliptic and parabolic coordinate systems on the plane. |
| first_indexed | 2024-04-12T18:39:09Z |
| format | Article |
| id | doaj.art-f4b69189d0eb4c08b9d8f54a42acee20 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-12T18:39:09Z |
| publishDate | 2012-05-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-f4b69189d0eb4c08b9d8f54a42acee202022-12-22T03:20:50ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-05-018031Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic CoordinatesAndrey V. TsiganovRecently we proposed a generic construction of the additional integrals of motion for the Stäckel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for elliptic and parabolic coordinate systems on the plane.http://dx.doi.org/10.3842/SIGMA.2012.031bilitysuperintegrabilityseparation of variablesAbel equationsaddition theorems |
| spellingShingle | Andrey V. Tsiganov Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates Symmetry, Integrability and Geometry: Methods and Applications bility superintegrability separation of variables Abel equations addition theorems |
| title | Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates |
| title_full | Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates |
| title_fullStr | Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates |
| title_full_unstemmed | Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates |
| title_short | Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates |
| title_sort | superintegrable stackel systems on the plane elliptic and parabolic coordinates |
| topic | bility superintegrability separation of variables Abel equations addition theorems |
| url | http://dx.doi.org/10.3842/SIGMA.2012.031 |
| work_keys_str_mv | AT andreyvtsiganov superintegrablestackelsystemsontheplaneellipticandparaboliccoordinates |