4 show that c ct ct c 8 ecker delta where c

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Unformatted text preview: epqj = 2oij. 4. Show that . c . CT = CT,.; C = 8, ecker delta. where C is the direction cosine matrx and 8 is the matrx of the Kron use it Any matrx obeying spch a relationship is called an orthogonal matri beca represents transformation of one set of ortogonal axes into another. 5. Show that for a second-order tensor A, the following thee quantities are Multiplication and Contraction of Tensors invarant under the rotation of axes: II = A¡¡ I A.2 A33 A31 Al3 /z = I Aii A12 I + A32 A23/ + I AiiA33 1 A21 A22 13 = det(A¡j). 4 3. Prove the following relationships: Ch 2: Problem 4 OijOij = 3 epqrepqr = 6 epq¡epqj = 2oij. 4. Show that . c . CT = CT,.; C = 8, ecker delta. where C is the direction cosine matrx and 8 is the matrx of the Kron use it Any matrx obeying spch a relationship is called an orthogonal matri beca represents transformation of one set of ortogonal axes into another. 5. Show that for a second-order tensor A, the following thee quantities are invarant under the rotation of axes: II = A¡...
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This document was uploaded on 02/28/2014 for the course PHYS 4200 at Columbia.

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