Bäcklund Transformations for the Kirchhoff Top
We construct Bäcklund transformations (BTs) for the Kirchhoff top by taking advantage of the common algebraic Poisson structure between this system and the sl(2) trigonometric Gaudin model. Our BTs are integrable maps providing an exact time-discretization of the system, inasmuch as they preserve bo...
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146705 |
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| Zitieren: | Bäcklund Transformations for the Kirchhoff Top / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1467052019-02-11T01:25:06Z Bäcklund Transformations for the Kirchhoff Top Ragnisco, O. Zullo, F. We construct Bäcklund transformations (BTs) for the Kirchhoff top by taking advantage of the common algebraic Poisson structure between this system and the sl(2) trigonometric Gaudin model. Our BTs are integrable maps providing an exact time-discretization of the system, inasmuch as they preserve both its Poisson structure and its invariants. Moreover, in some special cases we are able to show that these maps can be explicitly integrated in terms of the initial conditions and of the ''iteration time'' n. Encouraged by these partial results we make the conjecture that the maps are interpolated by a specific one-parameter family of hamiltonian flows, and present the corresponding solution. We enclose a few pictures where the orbits of the continuous and of the discrete flow are depicted. 2011 Article Bäcklund Transformations for the Kirchhoff Top / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J35; 70H06; 70H15 DOI:10.3842/SIGMA.2011.001 http://dspace.nbuv.gov.ua/handle/123456789/146705 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 construct Bäcklund transformations (BTs) for the Kirchhoff top by taking advantage of the common algebraic Poisson structure between this system and the sl(2) trigonometric Gaudin model. Our BTs are integrable maps providing an exact time-discretization of the system, inasmuch as they preserve both its Poisson structure and its invariants. Moreover, in some special cases we are able to show that these maps can be explicitly integrated in terms of the initial conditions and of the ''iteration time'' n. Encouraged by these partial results we make the conjecture that the maps are interpolated by a specific one-parameter family of hamiltonian flows, and present the corresponding solution. We enclose a few pictures where the orbits of the continuous and of the discrete flow are depicted. |
| format |
Article |
| author |
Ragnisco, O. Zullo, F. |
| spellingShingle |
Ragnisco, O. Zullo, F. Bäcklund Transformations for the Kirchhoff Top Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ragnisco, O. Zullo, F. |
| author_sort |
Ragnisco, O. |
| title |
Bäcklund Transformations for the Kirchhoff Top |
| title_short |
Bäcklund Transformations for the Kirchhoff Top |
| title_full |
Bäcklund Transformations for the Kirchhoff Top |
| title_fullStr |
Bäcklund Transformations for the Kirchhoff Top |
| title_full_unstemmed |
Bäcklund Transformations for the Kirchhoff Top |
| title_sort |
bäcklund transformations for the kirchhoff top |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146705 |
| citation_txt |
Bäcklund Transformations for the Kirchhoff Top / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 13 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ragniscoo backlundtransformationsforthekirchhofftop AT zullof backlundtransformationsforthekirchhofftop |
| first_indexed |
2025-07-11T00:27:31Z |
| last_indexed |
2025-07-11T00:27:31Z |
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1837308210658148352 |