AE321_ch1_2008 - Chapter 1 Mathematical Preliminaries Table...

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1 1. AE 321 Chapter 1 - Mathematical Preliminaries Table of contents 1.1 Review of vector theory 1.1.1 Vector algebra 1.1.2 Scalar and vector fi elds 1.2 Indicial notation (1.2-1.3) 1.3 Tensor theory 1.3.1 Coordinate transformation (1.4) 1.3.2 Cartesian tensors (1.5, 1.7, 1.8) * Numbers in parentheses refer to chapters in “Elasticity: Theory, Applications and Numerics” by M. H. Sadd
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2 1. AE 321 1.1.1 Vector Algebra Vector : Directed line segment Magnitude and direction r A = A x r e x + A y r e y + A z r e z = r r e r + A z r e z r e x , r e y , r e z : unit basis vectors for ( x , y , z ) or ( x 1 , x 2 , x 3 ) A x A y A z r e x r e y r e z x y z r A r ±
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3 1. AE 321 r A = A x r e x + A y r e y + A z r e z • Magnitude: A = r A = A x 2 + A y 2 + A z 2 r B = B x r e x + B y r e y + B z r e z • Vector multiplication: