From $\mathfrak{su}(2)$ 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) $\mathfrak{su}(2)$ Gaudin models. The procedure preserves the linear $r$-matrix formulation of the ancestor models. We give the Lax representation of the resultingintegrable systems in terms of $\mathfrak{su}(2)$ Lax matrices with and elliptic dependencies on the spectral parameter. We finally give some results about the many-body extensions of the constructed systems.