Geodesic
One-dimensional Lagrangians generated by a~quadratic form
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2009), pp. 33-44.

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

In this paper we apply the classical variational calculus to the Lagrangians of particular type. Namely, we establish formulas for the 1$^\mathrm{st}$ integrals and propose a technique for obtaining invariant 1$^\mathrm{st}$ integrals. We also deduce the differential homogeneity conditions for Lagrangians with respect to multiplication of the path $x(t)$ by the function $c(t)$ and with respect to the change of the parameter $t=t(s)$.
Keywords: conformally connected manifold, integral functionals, isotropic extreme curve, one-dimensional Lagrangians, path, quadratic form
Mots-clés : Euler–Lagrange equation, orthogonal group, scalar product. 
@article{IVM_2009_5_a3,
     author = {V. A. Luk'yanov},
     title = {One-dimensional {Lagrangians} generated by a~quadratic form},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--44},
     publisher = {mathdoc},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_5_a3/}
}
TY  - JOUR
AU  - V. A. Luk'yanov
TI  - One-dimensional Lagrangians generated by a~quadratic form
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 33
EP  - 44
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_5_a3/
LA  - ru
ID  - IVM_2009_5_a3
ER  - 
%0 Journal Article
%A V. A. Luk'yanov
%T One-dimensional Lagrangians generated by a~quadratic form
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 33-44
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_5_a3/
%G ru
%F IVM_2009_5_a3
V. A. Luk'yanov. One-dimensional Lagrangians generated by a~quadratic form. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2009), pp. 33-44. http://geodesic.mathdoc.fr/item/IVM_2009_5_a3/

[1] Krivonosov L. N., Razvitie konformnoi teorii polya, Dep. v VINITI No 1005-B92, Nizhegorodsk. gos. ped. un-t, 1992, 59 pp.

[2] Griffits F., Vneshnie differentsialnye sistemy i variatsionnoe ischislenie, Per. s angl., Mir, M., 1986, 360 pp. | MR

[3] Elsgolts L. E., Variatsionnoe ischislenie, GITTL, M., 1958, 162 pp.