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unit2_math_aside - 16.21 Techniques of Structural Analysis...

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Unformatted text preview: 16.21 Techniques of Structural Analysis and Design Spring 2005 Unit #2 - Mathematical aside: Vectors, indicial notation and summation convention Ra´ul Radovitzky February 6, 2005 Indicial notation In 16.21 we’ll work in a an euclidean three-dimensional space R 3 . Free index: A subscript index () i will be denoted a free index if it is not repeated in the same additive term where the index appears. Free means that the index represents all the values in its range. • Latin indices will range from 1 to, ( i, j, k, ... = 1 , 2 , 3), • greek indices will range from 1 to 2, ( α, β, γ, ... = 1 , 2). Examples: 1. a i 1 implies a 11 , a 21 , a 31 . (one free index) 2. x α y β implies x 1 y 1 , x 1 y 2 , x 2 y 1 , x 2 y 2 (two free indices). 3. a ij implies a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , a 33 (two free indices implies 9 values). 4. ∂σ ij + b i = 0 ∂x j 1 has a free index ( i ), therefore it represents three equations: ∂σ 1 j + b 1 = 0 ∂x j ∂σ 2 j...
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This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.

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unit2_math_aside - 16.21 Techniques of Structural Analysis...

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