Summary
The fundamentals of Cauchy continuum mechanics are set into discussion in view of unifying the methods of classical and relativistic field theory.
From a general variational principle—also valid for history-dependent materials—a set of four Euler-Lagrange equations are obtained. Noether's Erster Satz supplies, ten (actually reducing to seven) further equalities which, combined with the previous ones, yield the conservation laws of the field theory, expressing the properties of invariance of physical laws with respect to infinitesimal transformations of the reference frame. Some topics are discussed, concerning conservation laws in classical field theory.
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Capurro, M. A general field theory of cauchy continuum: Classical mechanics. Acta Mechanica 49, 169–190 (1983). https://doi.org/10.1007/BF01236349
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DOI: https://doi.org/10.1007/BF01236349