Geodesic
On the first Newton law, the existence of the reference system corresponding to the rest, and the Galilei group
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 389-394 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the Russian scientific literature, the authors carefully avoided mentioning the fact that Ernst Mach's assertion of 1904 about the meaninglessness of the concepts of uniform motion and absolute time in and of themselves has never been challenged in classical (not quantum) mechanics. Using hydrodynamics as an example, V. I. Arnold showed that a system of coordinates in which some finite volume of the medium is at rest exists almost always. We interpret this result as the existence of a system of coordinates in which all particles are at rest (the rest frame).
Keywords: continuum, Lagrangian and Eulerian descriptions, reference frame and system of coordinates, Noether theorem.
Mots-clés : Galilei group 
@article{TMF_2021_209_2_a10,
     author = {V. P. Pavlov},
     title = {On the~first {Newton} law, the~existence of the~reference system corresponding to the~rest, and {the~Galilei} group},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {389--394},
     year = {2021},
     volume = {209},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a10/}
}
TY  - JOUR
AU  - V. P. Pavlov
TI  - On the first Newton law, the existence of the reference system corresponding to the rest, and the Galilei group
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 389
EP  - 394
VL  - 209
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a10/
LA  - ru
ID  - TMF_2021_209_2_a10
ER  - 
%0 Journal Article
%A V. P. Pavlov
%T On the first Newton law, the existence of the reference system corresponding to the rest, and the Galilei group
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 389-394
%V 209
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a10/
%G ru
%F TMF_2021_209_2_a10
V. P. Pavlov. On the first Newton law, the existence of the reference system corresponding to the rest, and the Galilei group. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 389-394. http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a10/

[1] I. Nyuton, Matematicheskie nachala naturalnoi filosofii, Nauka, M., 1989 | MR | Zbl | Zbl

[2] V. A. Fok, Teoriya prostranstva, vremeni i tyagoteniya, GIFML, M., 1961 | MR

[3] E. Makh, Mekhanika. Istoriko-kriticheskii ocherk ee razvitiya, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2000 | MR

[4] V. I. Arnold, Obyknovennye differentsialnye uravneniya, Nauka, M., 1971 | MR

[5] K. Trusdell, Pervonanachalnyi kurs ratsionalnoi mekhaniki sploshnykh sred, Mir, M., 1975 | Zbl

[6] L. D. Faddeev, “Problema energii v teorii tyagoteniya Einshteina”, UFN, 136:3 (1982), 435–457 | DOI | DOI

[7] L. I. Sedov, Mekhanika sploshnoi sredy, v. 1, Nauka, M., 1970 | MR

[8] M. E. Eglit (red.), Mekhanika sploshnykh sred v zadachakh, v. 1, 2, Moskovskii litsei, M., 1996 | MR | Zbl

[9] I. G. Petrovskii, Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Fizmatlit, M., 2009 | MR

[10] L. S. Pontryagin, Obyknovennye differentsialnye uravneniya, Nauka, M., 1982 | MR | MR | Zbl | Zbl

[11] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki, v. VI, Gidrodinamika, Fizmatlit, M., 2015 | MR | MR