EN0175-06

EN0175-06 - EN0175 09 / 21 / 06 We continue on the...

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Unformatted text preview: EN0175 09 / 21 / 06 We continue on the mathematical background. Base tensors: (dyadic form) j i e e v v = 1 1 1 e e v v , , = 1 2 1 e e v v = 1 3 1 e e v v Note that: i j j i e e e e v v v v , ( ) T i j j i e e e e v v v v Rules of operation: ( ) ( ) i jk k j i k j i e e e e e e e v v v v v v v = = ( ) ( ) j ki j i k j i k e e e e e e e v v v v v v v = = Tensor product of vectors (also called tensor dyad): ( ) ( ) ( ) = = = 3 3 2 3 1 3 3 2 2 2 1 2 3 1 2 1 1 1 b a b a b a b a b a b a b a b a b a e e b a e b e a b a j i j i j j i i v v v v v v We can compare the matrix forms of different vector products: [ ] 3 3 2 2 1 1 3 2 1 3 2 1 b a b a b a b b b a a a b a + + = = v v [ ] = = 3 3 2 3 1 3 3 2 2 2 1 2 3 1 2 1 1 1 3 2 1 3 2 1 b a b a b a b a b a b a b a...
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This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.

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EN0175-06 - EN0175 09 / 21 / 06 We continue on the...

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