  Relations between the free motion on the GL^+(n, R) group manifold and the
dynamics of an n-particle system with spin degrees of freedom on a line
interacting with the pairwise 1/sinh^2 x ``potential''
(Euler-Calogero-Sutherland model) is discussed in the framework of Hamiltonian
reduction. Two kinds of reductions of the degrees of freedom are considered:
due to the continuous invariance and due to the discrete symmetry. It is shown
that after projection on the corresponding invariant manifolds the resulting
Hamiltonian system represents the Euler-Calogero-Sutherland model in both
cases.
