Use of the variational equation in the study of polarizable and magnetizable continuous media: PMM vol. 37, n≗5, 1973, pp. 803–812

Abstract

A model of a continuum is constructed, using the variational equation suggested in [1, 2] which makes it possible to obtain models of continua using a minimum number of unified physical hypotheses. In the present paper the variational equation is used to obtain a system of equations defining the macroscopic motion of a continuum with polarization and magnetization effects taken into account, within the framework of the special relativity theory. Use of the four-dimensional space-time and special relativity theory is required in order to match theories of electromagnetism and mechanics. We investigate some of the consequences of two possible decompositions of the total energy-momentum tensor of the electromagnetic field and the continuum into the continuum energy-momentum tensor and the electromagnetic field energy-momentum tensor according to Minkowski and to Abraham, respectively. When moment stresses and external mass moments are absent in the medium, we assume the symmetry of the total energy-momentum tensor of electromagnetic field and medium (this is equivalent to the absence or constancy of the combined electromagnetic field and medium, intrinsic internal moments of momenta along the world lines) and on this assumption consider certain models of continua.