[Manual] J. R. Barber - Elasticity, Solution Manual
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[Manual] J. R. Barber - Elasticity, Solution Manual , [Manual] J. R. Barber - Elasticity, Solution Manual기타솔루션 , 솔루션
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[Manual] J. R. Barber - Elasticity, Solution Manual
[Manual] J. R. Barber - Elasticity, Solution Manual
CHAPTER 1
1.1. Show that (i) √ ∂xi = δij and (ii) R = xi xi , ∂xj
where R = |R| is the distance from the origin. Hence nd ∂R/∂xj in index notation. Conrm your result by nding ∂R/∂x in x, y, z notation. For an orthogonal co¨rdinate system, o ∂x =0 ∂y (this is what is meant by orthogonality) and ∂x =1. ∂x In index notation, these results can be combined as ∂xi = δij . ∂xj The distance from the origin is R= x2 + x2 + x2 = 1 2 3 √ xi xi .
Combining these results, we have 1 ∂ √ ∂xi ∂xi xi xi =
CHAPTER 1
1.1. Show that (i) √ ∂xi = δij and (ii) R = xi xi , ∂xj
where R = |R| is the distance from the origin. Hence nd ∂R/∂xj in index notation. Conrm your result by nding ∂R/∂x in x, y, z notation. For an orthogonal co¨rdinate system, o ∂x =0 ∂y (this is what is meant by orthogonality) and ∂x =1. ∂x In index notation, these results can be c…(drop)
다.