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Journal of Physical Studies 7(1), 27–39 (2003)
DOI: https://doi.org/10.30970/jps.07.27 VARIATIONAL FORMULATION AND SYMMETRIES OF THE RELATIVISTIC NONDISSIPATIVE CONTINUUMV. I. Tretyak
Institute for Condensed Matter Physics of the National Academy
of Sciences of Ukraine |
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The Poincaré-invariance conditions for the variational description of the nondissipative continuum are formulated and analyzed. A general structure of the Lagrangian function, which provides such invariance and depends on the derivatives not higher than the first order, is indicated. By means of the Noether theorem we got ten conservation laws, the appearance of which, specifically, sets a structure of the energy-momentum tensor of the system. A transition from Lagrangean to Eulerian variables is discussed. It is shown that postulating additional symmetries allows formulating particular models of the relativistic continuum, especially the hydrodynamics and isotropic body model.
PACS number(s): 03.30.+p, 46.05.+b, 47.10.+g