TEST BANK FOR Elasticity By J. R. Barber Converted
Chamberlian School of Nursing
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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...
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