Geometrization of the scleronomic Riemannian mechanical systems

The paper is devoted to the geometrical theory, on the phase space, of the classical concept of scleronomic Riemannian mechanical systems in the general case when the external forces depend on the material points and their velocities. We discuss the canonical semispray, the nonlinear connection, the metrical connection, the electromagnetic field and the almost Hermitian model of the mentioned mechanical system. Based on the methods of Lagrange geometry we prepare here the framework for the investigation of the geometrical theory of Riemannian mechanical systems whose external forces depend on the accelerations of order k ≥ 1. M.S.C. 2010: 53B40,53C60.