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.
Petrera, M., Ragnisco, O. (2007). From su(2) Gaudin Models to Integrable Tops. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 3.
From su(2) Gaudin Models to Integrable Tops
RAGNISCO, Orlando
2007-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
