2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153787Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.2 pages, AMS-TeX, version 2.1, size 6 Kbytes (ASCII). Report on 16-th joint session of Seminar of I.G. Petrovsky and Moscow Mathematical Society at Moscow State University. January 19, 1994. To be published in: Uspehi Mat. NaukExactly Solvable and Integrable SystemsAlgebraic GeometryAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext