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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, Volume 13, Issue 4(1), Pages 96–102
DOI: https://doi.org/10.18500/1816-9791-2013-13-4-96-102
(Mi isu449)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mechanics

Rotational invariance of non-linear Lagrangians of type-II micropolar thermoelastic continuum

Y. N. Radayeva, V. A. Kovalevb

a Institute for Problems in Mechanics of the Russian Academy of Sciences, Russia, 119526, Moscow, pr. Vernadskogo, 101, block 1
b Moscow City Government University of Management Moscow, Russia, 107045, Moscow, Sretenka st., 28
Full-text PDF (145 kB) Citations (1)
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Abstract: The paper contains new results related to extension of the field theoretical approach and its formalism to non-linear coupled micropolar thermoelastic media. A mathematical model of micropolar (MP) type-II (GNII) thermoelastic (TE) continuum is considered. A formulation of the least thermoelastic action principle is discussed. Partial differential equations subsequent to the least action principle are derived. The translational symmetries of non-linear Lagrangians are adopted. Those include an additional symmetry: translations of the thermal displacement. The rotational invariance of the action and corresponding Lagrangian is then studied. For micropolar type-II thermoelastic Lagrangians following the usual procedure independent rotationally invariant functional arguments are obtained. Objective forms of the Lagrangians satisfying the frame indifference principle are given.
Key words: type-II micropolar thermoelasticity, field, extra field, action, Lagrangian, $d$-vector, invariance, rotation, frame indifference principle, deformation, extra deformation.
Bibliographic databases:
Document Type: Article
UDC: 539.374
Language: Russian
Citation: Y. N. Radayev, V. A. Kovalev, “Rotational invariance of non-linear Lagrangians of type-II micropolar thermoelastic continuum”, Izv. Saratov Univ. Math. Mech. Inform., 13:4(1) (2013), 96–102
Citation in format AMSBIB
\Bibitem{RadKov13}
\by Y.~N.~Radayev, V.~A.~Kovalev
\paper Rotational invariance of non-linear Lagrangians of type-II micropolar thermoelastic continuum
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2013
\vol 13
\issue 4(1)
\pages 96--102
\mathnet{http://mi.mathnet.ru/isu449}
\crossref{https://doi.org/10.18500/1816-9791-2013-13-4-96-102}
\elib{https://elibrary.ru/item.asp?id=21133485}
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  • This publication is cited in the following 1 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:332
    Full-text PDF :98
    References:59
     
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