B\"acklund transformations for the rational Lagrange chain

We consider a long–range homogeneous chain where the local variables are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting Lagrange tops. We call this classical integrable model rational ``Lagrange chain’’ showing how one can obtain it starting from $\mathfrak{s}\mathfrak{u}(2)$ rational Gaudin models. Moreover we construct one- and two–point integrable maps (B"acklund transformations).