  It is shown that geodesic motion on the GL(n, R) group manifold endowed with
the bi-invariant metric d s^2 = tr(g^{-1} d g)^2 corresponds to a
generalization of the hyperbolic n-particle Calogero-Moser-Sutherland model. In
particular, considering the motion on Principal orbit stratum of the SO(n, R)
group action, we arrive at dynamics of a generalized n-particle
Calogero-Moser-Sutherland system with two types of internal degrees of freedom
obeying SO(n, R) \bigoplus SO(n, R) algebra. For the Singular orbit strata of
SO(n, R) group action the geodesic motion corresponds to certain deformations
of the Calogero-Moser-Sutherland model in a sense of description of particles
with different masses. The mass ratios depend on the type of Singular orbit
stratum and are determined by its degeneracy. Using reduction due to discrete
and continuous symmetries of the system a relation to II A_n
Euler-Calogero-Moser-Sutherland model is demonstrated.
