Geodesic
Multidimensional dynamical systems accepting the normal shift
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 2, pp. 264-269

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Dynamical systems $\ddot {\mathbf r} = \mathbf F(\mathbf r, \dot {\mathbf r})$ in $\mathbb R^n$ accepting the normal shift of submanifolds of codimension 1 are considered. The concept of weak normality for them is introduced and the defining partial differential equations for the force field $\mathbf F(\mathbf r,\dot {\mathbf r})$ of the dynamical systems with the weak and complete normality are found. 
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     author = {A. Yu. Boldin and R. A. Sharipov},
     title = {Multidimensional dynamical systems accepting the normal shift},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {264--269},
     publisher = {mathdoc},
     volume = {100},
     number = {2},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a8/}
}
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A. Yu. Boldin; R. A. Sharipov. Multidimensional dynamical systems accepting the normal shift. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 2, pp. 264-269. http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a8/