  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 $\mathfrak{su}(2)$ rational Gaudin
models. Moreover we construct one- and two--point integrable maps (B\"acklund
transformations).
