Construction of the classical $R$-matrices for the Toda and Calogero models

We use the definition of the Calogero–Moser models as Hamiltonian reductions of geodesic motions on a group manifold to construct their $R$-matrices. In the Toda case, the analogous construction yields constant $R$-matrices. By contrast, for Calogero–Moser models they are dynamical objects.