TEST BANK FOR Elasticity By J. R. Barber Converted
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Exam (elaborations) TEST BANK FOR Elasticity By J. R. Barber (Solution Manual)-Converted
- Exam (elaborations) • 217 pages • 2021
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1.1. Show that
(i)
∂xi
∂xj
= δij and (ii) R = √xixi ,
where R = |R| is the distance from the origin. Hence find ∂R/∂xj in index
notation. Confirm your result by finding ∂R/∂x in x, y, z notation.
For an orthogonal co¨ordinate system,
∂x
∂y
= 0
(this is what is meant by orthogonality) and
∂x
∂x
= 1 .
In index notation, these results can be combined as
∂xi
∂xj
= δij .
The distance from the origin is
R =
q
x2
1 + x2
2 + x2
3 = √xixi .
Combini...
Exam (elaborations)
Exam (elaborations) TEST BANK FOR Elasticity By J. R. Barber (Solution Manual)-Converted
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1.1. Show that (i) ∂xi ∂xj = δij and (ii) R = √xixi , where R = |R| is the distance from the origin. Hence find ∂R/∂xj in index notation. Confirm your result by finding ∂R/∂x in x, y, z notation. For an orthogonal co¨ordinate system, ∂x ∂y = 0 (this is what is meant by orthogonality) and ∂x ∂x = 1 . In index notation, these results can be combined as ∂xi ∂xj = δij . The distance from the origin is R = q x2 1 + x2 2 + x2 3 = √xixi . Combini...
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