Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 058, 14 pages      math-ph/0703044      https://doi.org/10.3842/SIGMA.2007.058
Contribution to the Vadim Kuznetsov Memorial Issue

From su(2) Gaudin Models to Integrable Tops

Matteo Petrera a and Orlando Ragnisco b
a) Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, D-85747 Garching bei München, Germany
b) Dipartimento di Fisica E. Amaldi, Università degli Studi Roma Tre and Sezione INFN, Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

Received March 13, 2006; Published online April 20, 2007

Abstract
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.

Key words: Gaudin models; spinning tops.

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