 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 57, Issue 6 / 2022 | Next article >> |
| E.V. Murashkin and Yu.N. Radayev, "An Algebraic Algorithm of Pseudotensors Weights Eliminating and Recovering," Mech. Solids. 57 (6), 1416-1423 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
6 |
Pages |
1416-1423 |
| DOI |
10.3103/S0025654422060085 |
| Title |
An Algebraic Algorithm of Pseudotensors Weights Eliminating and Recovering |
| 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 |
The paper deals with an algebraic algorithm for the pseudotensors weights eliminating and recovering. The proposed algorithm allows us to reduce pseudotensors of arbitrary ranks and weights to absolute tensors of higher ranks. The weight of a pseudotensor is assumed to be an integer (positive or negative). The algorithm is based on the transformation of a pseudotensor of arbitrary rank and integer weight by using tensor product of permutation symbols. The requisite equations from algebra and analysis of pseudotensors are given and discussed. Based on the proposed algebraic algorithm, covariant constancy of permutation symbols and fundamental orienting pseudoscalar powers, a realisation of covariant differentiation of a pseudotensor field of arbitrary rank and integer weight is developed. The definition of the pseudotensor field gradient is then introduced. |
| Keywords |
pseudotensor, integer weight, fundamental orienting pseudoscalar, permutation symbol, covariant derivative, gradient, nabla operator |
| Received |
09 June 2022 | Revised |
10 July 2022 | Accepted |
11 August 2022 |
| Link to Fulltext |
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