Geodesic
Lagrangian classical relativistic mechanics of~a~system of~directly interacting particles.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 2, pp. 194-208

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

General formulation of the one-time Lagrangian relativistic classical description of $N$ directly interacting particles is developed. A representation of a continuous transformation group of the Minkowski space (in particular, Poincare group) by the Lie–Backlund tangent transformations of the configuration space of the system is constructed. By means of this representation the system of linear differential equations expressing the Poincare invariance of the Lagrangian formalism is obtained and corresponding restrictions on the form of the generalised Lagrangian are studied. The exact relativistic description of the interaction is shown to demand the dependence of the Lagrangian on the infinite order derivatives. The results will be used in the second part of the work for finding a general form of the approximate relativistic interaction Lagrangian and for working out the method of constructing the Poincare invariant Newton type equations of motion and their first integrals. 
@article{TMF_1980_44_2_a4,
     author = {R. P. Gaida and Yu. B. Klyuchkovskii and V. I. Tretyak},
     title = {Lagrangian classical relativistic mechanics of~a~system of~directly interacting {particles.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {194--208},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a4/}
}
TY  - JOUR
AU  - R. P. Gaida
AU  - Yu. B. Klyuchkovskii
AU  - V. I. Tretyak
TI  - Lagrangian classical relativistic mechanics of~a~system of~directly interacting particles.~I
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1980
SP  - 194
EP  - 208
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a4/
LA  - ru
ID  - TMF_1980_44_2_a4
ER  - 
%0 Journal Article
%A R. P. Gaida
%A Yu. B. Klyuchkovskii
%A V. I. Tretyak
%T Lagrangian classical relativistic mechanics of~a~system of~directly interacting particles.~I
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 194-208
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a4/
%G ru
%F TMF_1980_44_2_a4
R. P. Gaida; Yu. B. Klyuchkovskii; V. I. Tretyak. Lagrangian classical relativistic mechanics of~a~system of~directly interacting particles.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 2, pp. 194-208. http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a4/