Geodesic
Center-of-mass variables in the relativistic Lagrangian dynamics of a system of particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 3, pp. 402-416

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To separate the motion of a relativisticN-particle system as a whole from its internal motion, we propose center-of-mass variables in an arbitrary (geometrical) form of Lagrangian dynamics. In terms of these variables, we construct a representation of the Poincaré group $\mathcal P(1.3)$ by Lie–Bäcklund vector fields; we find expressions for transformation of the center-of-mass variables under the influence of finite transformations of this group. We obtain a class of Lagrangians that depend on derivatives of not higher than the second order. We construct ten conservation laws corresponding to the symmetry with respect to $\mathcal P(1.3)$P. We analyze the motion of the system as a whole. The transition to the Hamiltonian description is considered. 
@article{TMF_1994_101_3_a8,
     author = {R. P. Gaida and V. I. Tretyak and Yu. G. Yaremko},
     title = {Center-of-mass variables in the relativistic {Lagrangian} dynamics of a system of particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {402--416},
     publisher = {mathdoc},
     volume = {101},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_101_3_a8/}
}
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R. P. Gaida; V. I. Tretyak; Yu. G. Yaremko. Center-of-mass variables in the relativistic Lagrangian dynamics of a system of particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 3, pp. 402-416. http://geodesic.mathdoc.fr/item/TMF_1994_101_3_a8/