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This article discusses a possibility of deriving the basic equations of electrodynamics by means of the rational continuum mechanics principles and methods. We show that in order to give rise to the challenge, one needs to consider an elastic continuum of two‐spin particles of a special kind. We derive classical Maxwell's equations and discuss reasons limiting their application. After that, we propose...
The electromagnetic fields (D, H) represent contravariant components of an antisymmetric 4‐tensor, while the fields (E, B) represent covariant components of the same 4‐tensor. Both sets are identical in Lorentz frames. The governing equations for them represent equations of balance for the flux of D and the flux B across open surfaces and they are invariant under arbitrary analytic transformation...
This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material. The spatial point‐of‐view for the description of fields...
A nonlinear model of an electrically conductive micropolar medium interacting with an external magnetic field is proposed. The deformable state of such a medium is described by two asymmetric tensors: tensor of deformations and bending‐torsion tensor. Both tensors consider both linear and nonlinear terms in rotation and displacement gradients (geometric nonlinearity). The components of the bending‐torsion...
We consider a special type Cosserat continuum and suggest analogies between quantities characterizing the stress–strain state of the continuum and quantities characterizing physical processes. Such an approach provides us with the ability to derive equations describing electricity, magnetism, and other physical phenomena. This study continues the line of our earlier research. In the present paper,...
We propose and examine a potential analogy between mass transfer (in space) and energy transfer (in solids). We adapt classical equations of matter dynamics to describe the dynamics of energy transfer. Such fundamental quantities as the effective mass, momentum, moment of inertia and other quantities typical for bodies of matter are introduced for “bodies” of energy. Along with this, two new concepts...
The dynamics of an incompressible, isotropic elastic continuum are discussed. Starting from the Lorentz‐invariant motion of defects in elastic continua, MacCullagh's aether theory (1839) of an incompressible elastic solid is reconsidered. Since MacCullagh's theory, based on linear elasticity, cannot describe charges, particular attention is given to a topological defect that causes large deformations...
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