We study a quite general family of dynamical r-matrices for an auxiliary
loop algebra L(su(2)) related to restricted flows for equations of
the KdV type. This underlying r-matrix structure allows to reconstruct Lax
representations and to find variables of separation for a wide set of the
integrable natural Hamiltonian systems. As an example, we discuss the
Henon-Heiles system and a quartic system of two degrees of freedom in detail.Comment: 25pp, LaTe