 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| E.V. Murashkin and Yu.N. Radayev, "On the Theory of Covariant Differentiation of Two Point Pseudotensor Fields," Mech. Solids. 57 (6), 1365-1373 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
6 |
Pages |
1365-1373 |
| DOI |
10.3103/S0025654422060255 |
| Title |
On the Theory of Covariant Differentiation of Two Point Pseudotensor Fields |
| Author(s) |
E.V. Murashkin (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, evmurashkin@gmail.com)
Yu.N. Radayev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru) |
| Abstract |
In this paper, the problems of covariant differentiation of two-point pseudotensor fields of arbitrary ranks and weights are considered and discussed. The requisite equations and notions from algebra and analysis of pseudotensors are recalled. The notion of a two-point pseudotensor field is introduced, based on the equation for its transformation under changing coordinate net. An equation for the transformation of a two-point pseudotensor field to a two-point absolute tensor field is proposed. Definitions of total and explicit operators of partial and covariant differentiation of two-point pseudotensors are introduced. Equations for covariant derivatives of a two-point pseudotensor field are obtained. Important examples of two-point pseudotensor fields from non-linear solid mechanics are noted. |
| Keywords |
two-point pseudotensor, fundamental orienting pseudoscalar, covariant derivative, total Hamilton operator |
| Received |
09 June 2022 | Revised |
10 July 2022 | Accepted |
11 August 2022 |
| Link to Fulltext |
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