TEST BANK FOR Elasticity By J. R. Barber Converted

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...