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By Zlatko Jankocic

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Extra resources for A Contribution to the Vector and Tensor Analysis: Course Held at the Department for Mechanics of Deformable Bodies September – October 1969

Example text

We have e' E'< > ' e" = ei. E'< > E"<= ef- E''<.. (4. 6) > > / and similar relations for other basis vectors. The rela tions (4. 6) reflect the group character of the basis vector transformations, because for the transformation coeffi cients we explicitly have ( 4. 7) and similar sets of relations for other basis vectors. 30 Vector and Tensor Algebra CHAPTER V Tensors The results obtained for vec- tors can be extended to more general objects, tensors, in the following way. We take N vector spaces (

9i · 1n (1. 6). To illustrate the application, we add two simple examples. l) We assume that the particular case (2. 8) for spaces X (oo) and both X (C) is realized, i. e. 0 . , •. ( 6. 5) ~. Thus, for the two spaces the difference between cases A and B disappears. We introduce a one-to-one correspondence between the vectors of the two space s X(C) . TX ex t, f. = ')(e )C>

For the continuum the scheme (1. "m Chapt. ". e 43 X y e = g. Y)) , o(x-'Y) x9 y ( = 9 ( x' Y ) ) (6. o J' 7 i. 9i · 1n (1. 6). To illustrate the application, we add two simple examples. l) We assume that the particular case (2. 8) for spaces X (oo) and both X (C) is realized, i. e. 0 . , •. ( 6. 5) ~. Thus, for the two spaces the difference between cases A and B disappears. We introduce a one-to-one correspondence between the vectors of the two space s X(C) . TX ex t, f. = ')(e )C>

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