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Explicit description for arbitrary Newtonian dynamical system admitting thenormal shift in Riemannian manifold of the dimension $n\geq 3$ is found. On thebase of this result the kinematics of normal shift of hypersurfaces alongtrajectories of such system is studied.Comment: AmSTeX, 38 pages, amsppt styl

Newtonian normal shift in multidimensional Riemannian geometry