Geodesic
Generalized pseudotensor formulations of~the~Stokes' integral theorem
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 22 (2022) no. 2, pp. 205-215

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ISU_2022_22_2_a6,
     author = {Yu. N. Radayev and E. V. Murashkin},
     title = {Generalized pseudotensor formulations {of~the~Stokes'} integral theorem},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {205--215},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ISU_2022_22_2_a6/}
}
TY  - JOUR
AU  - Yu. N. Radayev
AU  - E. V. Murashkin
TI  - Generalized pseudotensor formulations of~the~Stokes' integral theorem
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2022
SP  - 205
EP  - 215
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2022_22_2_a6/
LA  - en
ID  - ISU_2022_22_2_a6
ER  - 
%0 Journal Article
%A Yu. N. Radayev
%A E. V. Murashkin
%T Generalized pseudotensor formulations of~the~Stokes' integral theorem
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2022
%P 205-215
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2022_22_2_a6/
%G en
%F ISU_2022_22_2_a6
Yu. N. Radayev; E. V. Murashkin. Generalized pseudotensor formulations of~the~Stokes' integral theorem. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 22 (2022) no. 2, pp. 205-215. http://geodesic.mathdoc.fr/item/ISU_2022_22_2_a6/