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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, Volume 9, Issue 4(2), Pages 41–94
DOI: https://doi.org/10.18500/1816-9791-2009-9-4-2-41-94
(Mi isu87)
 

This article is cited in 4 scientific papers (total in 4 papers)

Mechanics

Mathematical models and contemporary theories of physical fields

V. A. Kovaleva, Yu. N. Radayevb

a Moscow City Government University of Management, Chair of Applied Mathematics;
b Samara State University, Chair of Continuum Mechanics
Full-text PDF (720 kB) Citations (4)
References:
Abstract: Elements of the classical field theory based on a variational formulation of the Hamilton type are discussed and corresponding 4-dimensional Lagrange formalism is presented both as the variational and the group theoretical script. Variational symmetries (geometric and generalized) of field equations and theNoether theoremproviding a regular way of obtaining a conservation law for every given variational symmetry are revisited in the study in order to give a complete version of the contemporary field theory. All developments are presented in the non-linear frame (i.e. of finite strains as to continuum mechanics). Natural derivations of all tensor attributes of a physical field are given by the variational symmetry technique. The null Lagrangian theory for $n$-dimensional manifold (including 4-dimensional Minkowski space-time) is developed in an attempt to extend the canonical formalismof non-linear field theory. By the aid of divergence formula for the null Lagrangians regular in $n$-dimensional star-shaped domains, a general representation of the null Lagrangian depending as maximum on the first order field gradients is obtained. A method of systematic and derivation of the null Lagrangians for $n$-dimensional manifold is proposed. It is shown that in the case of non-linear 3-component field in 3-dimensional space the null Lagrangian is represented, in general, via 15 arbitrary independent field functions.
Key words: field theory, Lagrange formalism, variational principle, conservation law, null Lagrangian, group theoretical formalism.
Document Type: Article
UDC: 514.774.2:517.972/.974:539.3
Language: Russian
Citation: V. A. Kovalev, Yu. N. Radayev, “Mathematical models and contemporary theories of physical fields”, Izv. Saratov Univ. Math. Mech. Inform., 9:4(2) (2009), 41–94
Citation in format AMSBIB
\Bibitem{KovRad09}
\by V.~A.~Kovalev, Yu.~N.~Radayev
\paper Mathematical models and contemporary theories of physical fields
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2009
\vol 9
\issue 4(2)
\pages 41--94
\mathnet{http://mi.mathnet.ru/isu87}
\crossref{https://doi.org/10.18500/1816-9791-2009-9-4-2-41-94}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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    Abstract page:538
    Full-text PDF :198
    References:66
     
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