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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, Volume 22, Issue 2, Pages 205–215
DOI: https://doi.org/10.18500/1816-9791-2022-22-2-205-215
(Mi isu934)
 

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

Scientific Part
Mechanics

Generalized pseudotensor formulations of the Stokes' integral theorem

Yu. N. Radayev, E. V. Murashkin

Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Prospekt Vernadskogo, Moscow 119526, Russia
Full-text PDF (526 kB) Citations (4)
References:
Abstract: Oriented continua play an important role in micropolar elasticity modelling. All realizations of micropolar theories are conceptually possible only within the framework of the pseudotensor formalism and the orientable manifold notion. This particularly concerns the theory of micropolar hemitropic elastic media. In this paper, a pseudotensor description is used in contrast to Kartan's formalism. The pseudotensor formulation of Stokes' integral theorem is almost unknown in the current scientific literature. Here we consider various formulations of Stokes' integral theorem for an arbitrary asymmetric covariant pseudotensor field of a given weight and valency. This extends the theorem to the case of pseudotensors. This fact makes it possible to use the mentioned generalization for micropolar continua. The study mostly relies on the class of special coordinate systems often employed in classical physical field theories. A procedure for orientations consistency inside and on the boundary of a manifold is discussed for various formulations of Stokes' integral theorem.
Key words: pseudotensor, fundamental orienting pseudoscalar, micropolar hemitropic continuum, $M$-cell, coordinate frame, Stokes' integral theorem, orientation consistency.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00666
Ministry of Science and Higher Education of the Russian Federation AAAA-A20-120011690132-4
The present study was financially supported by the state task (state registration No. AAAA-A20-120011690132-4) and with the support of the Russian Foundation for Basic Research (project No. 20-01-00666).
Received: 12.12.2021
Accepted: 24.02.2022
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: English
Citation: Yu. N. Radayev, E. V. Murashkin, “Generalized pseudotensor formulations of the Stokes' integral theorem”, Izv. Saratov Univ. Math. Mech. Inform., 22:2 (2022), 205–215
Citation in format AMSBIB
\Bibitem{RadMur22}
\by Yu.~N.~Radayev, E.~V.~Murashkin
\paper Generalized pseudotensor formulations of~the~Stokes' integral theorem
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2022
\vol 22
\issue 2
\pages 205--215
\mathnet{http://mi.mathnet.ru/isu934}
\crossref{https://doi.org/10.18500/1816-9791-2022-22-2-205-215}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4439111}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
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    Full-text PDF :46
    References:25
     
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