Abstract
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 groupP 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 toP. We analyze the motion of the system as a whole. The transition to the Hamiltonian description is considered.
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Additional information
Institute of Physics of Condensed Systems, Ukrainian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 3, pp. 402–416, December, 1994.
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Gaida, R.P., Tretyak, V.I. & Yaremko, Y.G. Center-of-mass variables in the relativistic Lagrangian dynamics of a system of particles. Theor Math Phys 101, 1443–1453 (1994). https://doi.org/10.1007/BF01035466
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DOI: https://doi.org/10.1007/BF01035466