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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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