From su(2) Gaudin Models to Integrable Tops

In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models. The procedure preserves the linear r-matrix formulation of t...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2007
Main Authors: Petrera, M., Ragnisco, O.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147380
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:From su(2) Gaudin Models to Integrable Tops / M. Petrera, O. Ragnisco // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 29 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Petrera, M.
Ragnisco, O.
author_facet Petrera, M.
Ragnisco, O.
citation_txt From su(2) Gaudin Models to Integrable Tops / M. Petrera, O. Ragnisco // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 29 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models. The procedure preserves the linear r-matrix formulation of the ancestor models. We give the Lax representation of the resulting integrable systems in terms of su(2) Lax matrices with rational and elliptic dependencies on the spectral parameter. We finally give some results about the many-body extensions of the constructed systems.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T20:25:35Z
publishDate 2007
publisher Інститут математики НАН України
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spelling Petrera, M.
Ragnisco, O.
2019-02-14T14:54:25Z
2019-02-14T14:54:25Z
2007
From su(2) Gaudin Models to Integrable Tops / M. Petrera, O. Ragnisco // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 29 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 70E17; 70E40; 37J35
https://nasplib.isofts.kiev.ua/handle/123456789/147380
In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models. The procedure preserves the linear r-matrix formulation of the ancestor models. We give the Lax representation of the resulting integrable systems in terms of su(2) Lax matrices with rational and elliptic dependencies on the spectral parameter. We finally give some results about the many-body extensions of the constructed systems.
This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. M.P. thanks Yuri B. Suris and G. Satta for helpful comments. M.P. was partially supported by the European Community through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652) and by the European Science Foundation project MISGAM.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
From su(2) Gaudin Models to Integrable Tops
Article
published earlier
spellingShingle From su(2) Gaudin Models to Integrable Tops
Petrera, M.
Ragnisco, O.
title From su(2) Gaudin Models to Integrable Tops
title_full From su(2) Gaudin Models to Integrable Tops
title_fullStr From su(2) Gaudin Models to Integrable Tops
title_full_unstemmed From su(2) Gaudin Models to Integrable Tops
title_short From su(2) Gaudin Models to Integrable Tops
title_sort from su(2) gaudin models to integrable tops
url https://nasplib.isofts.kiev.ua/handle/123456789/147380
work_keys_str_mv AT petreram fromsu2gaudinmodelstointegrabletops
AT ragniscoo fromsu2gaudinmodelstointegrabletops