Open AccessRepresentation of symmetric second-rank III tensor in the space of resultant eigenvectors
Author(s) -
Evgeniy E. Kuznetsov,
I. N. Matchenko,
N. M. Matchenko
Publication year - 2015
Publication title -
izvestiâ mgtu "mami"
Language(s) - English
Resource type - Journals
eISSN - 2949-1428
pISSN - 2074-0530
DOI - 10.17816/2074-0530-67152
Subject(s) - symmetric tensor , tensor (intrinsic definition) , eigenvalues and eigenvectors , cartesian tensor , rank (graph theory) , vector space , mathematics , basis (linear algebra) , space (punctuation) , tensor field , representation (politics) , tensor density , pure mathematics , normed vector space , tensor contraction , mathematical analysis , combinatorics , geometry , physics , tensor product , computer science , exact solutions in general relativity , quantum mechanics , politics , political science , law , operating system
The article examines the possibility of representation of a symmetric second rank III tensor in the three-dimensional vector space of resultant eigenvectors. It has been shown that the vector space of resultant eigenvalues consists of six independent segments. Vector symmetric tensor may be represented in any of the segments independently. The authors introduce a local vector basis for each of the sectors. It is shown that the previously proposed by A.A. Ilyushin and K.F. Chernykh vector basis of the stress tensor are the second and third segments of the vector space of principal stresses.