Geodesic
A problem on branchistochrone as invariant variational problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 92-96.

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

Based on the modified theory of invariant variational problems developed by the author, we describe a theoretical group approach to solving a problem of branchistochrone.
Mots-clés : branchistochrone, conformal invariance
Keywords: functional, first integral, infinitesimal operator, time of steepest descent. 
@article{IVM_2017_1_a9,
     author = {K. G. Garaev},
     title = {A problem on branchistochrone as invariant variational problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {92--96},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_1_a9/}
}
TY  - JOUR
AU  - K. G. Garaev
TI  - A problem on branchistochrone as invariant variational problem
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 92
EP  - 96
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_1_a9/
LA  - ru
ID  - IVM_2017_1_a9
ER  - 
%0 Journal Article
%A K. G. Garaev
%T A problem on branchistochrone as invariant variational problem
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 92-96
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_1_a9/
%G ru
%F IVM_2017_1_a9
K. G. Garaev. A problem on branchistochrone as invariant variational problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 92-96. http://geodesic.mathdoc.fr/item/IVM_2017_1_a9/

[1] Polak R. S., Variatsionnye printsipy mekhaniki, GIFML, M., 1960

[2] Akhiezer N. I., Lektsii po variatsionnomu ischisleniyu, GITTL, M., 1955

[3] Garaev K. G., “Zamechanie k teorii Nëter”, Izv. vuzov. Matem., 1989, no. 5, 69–71

[4] Noether E., “Invariant variational problems”, Gött. Nachr., 1918, 235–257 | MR | Zbl

[5] Bessel-Hagen E., “Über die Erhaltungssätze der Electrodynamik”, Math. Ann., 84:3–4 (1921), 258–276 | DOI | MR | Zbl

[6] Steudel H., “Eine Erweiterung des ersten Noetherschen Satzes”, Z. Naturforsch, 17A (1962), 133–135 | MR

[7] Ibragimov N. Kh., “Invariantnye variatsionnye zadachi i ikh zakony sokhraneniya”, Teoret. i matem. fizika, 1:3 (1969), 350–359 | MR