Geodesic
The problem of metrizability of dynamical systems that admit normal shift
Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 1, pp. 85-93 
R. A. Sharipov. The problem of metrizability of dynamical systems that admit normal shift. Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 1, pp. 85-93. http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a7/
@article{TMF_1994_101_1_a7,
     author = {R. A. Sharipov},
     title = {The problem of metrizability of dynamical systems that admit normal shift},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {85--93},
     year = {1994},
     volume = {101},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a7/}
}
TY  - JOUR
AU  - R. A. Sharipov
TI  - The problem of metrizability of dynamical systems that admit normal shift
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 85
EP  - 93
VL  - 101
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a7/
LA  - ru
ID  - TMF_1994_101_1_a7
ER  - 
%0 Journal Article
%A R. A. Sharipov
%T The problem of metrizability of dynamical systems that admit normal shift
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 85-93
%V 101
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1994_101_1_a7/
%G ru
%F TMF_1994_101_1_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of metrizability for the dynamical systems accepting the normal shift is formulated and solved. The explicit formula for the force-field of metrizable newtonian dynamical system $\partial _{tt}\mathbf r=\mathbf F(\mathbf r,\partial _t\mathbf r)$ is found.

[1] Boldin A. Yu., Sharipov R. A., TMF, 97:3 (1993), 386–395 | MR | Zbl

[2] Boldin A. Yu., Sharipov R. A., TMF, 100:2 (1994), 264–269 | MR | Zbl

[3] Bianchi L., Ann. Mat., 18:3 (1911), 185–243 | DOI | MR | Zbl

[4] Teneblat K., Bol. Soc. Bras. Math., 18:2 (1985), 67–92

[5] Levi-Civita T., Ann. Mat. {, ser. 2}, 24 (1896), 255–300 | DOI | Zbl

[6] Sinyukov N. S., Geodezicheskie otobrazheniya rimanovykh prostranstv, Nauka, M., 1979 | MR | Zbl

[7] Sinyukov N. S., “Pochti geodezicheskie otobrazheniya affinnosvyaznykh i rimanovykh prostranstv”, Itogi nauki i tekhniki. Problemy geometrii, 13, VINITI, M., 1982, 3–26 | MR | Zbl

[8] Aminova A. V., UMN, 48:2 (1993), 107 | MR | Zbl

[9] Petrov A. Z., Modelirovanie fizicheskikh polei, vyp. 4–5, Gravitatsiya i teoriya otnositelnosti, Kazanskii universitet, Kazan

[10] Petrov A.Z., DAN SSSR, 186:6 (1969), 1302–1305

[11] Petrov A. Z., DAN SSSR, 190:2 (1970), 305–308

[12] Petrov A. Z., K voprosu o modelirovanii polei gravitatsii, Preprint ITF-71-130 R, Institut teoreticheskoi fiziki, Kiev, 1971