From su(2) Gaudin Models to Integrable Tops

TL;DR

This paper derives classical integrable tops, including the Lagrange top and Clebsch system, from su(2) Gaudin models via algebraic contraction, preserving their algebraic structure and extending to many-body cases.

Contribution

It introduces a method to obtain integrable tops from Gaudin models through algebraic contraction, maintaining the r-matrix structure.

Findings

Derived Lax representations for integrable tops

Preserved algebraic structure during contraction

Extended models to many-body systems

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.