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- Title
Linear invariants of a Cartesian tensor.
- Authors
AHMAD, FAIZ; RASHID, MUNEER AHMAD
- Abstract
The number of linear invariants under SO(3) as well as SO(2) of a Cartesian tensor of an arbitrary rank is studied. A linear form is defined in terms of elements of a tensor. It is established that the number of linear invariants of a tensor of rank n under SO(3) equals the dimension of the space of isotropic tensors of rank n. Formulas for the number of invariants in the two cases are also derived. For the elasticity tensor, our analysis confirms the results of Norris.
- Subjects
MATHEMATICAL symmetry; ELASTICITY; INVARIANTS (Mathematics); TENSOR products; INVARIANT measures
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2009, Vol 62, Issue 1, p31
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbn021