Page 81 - Introduction to Continuum Mechanics

86 Curvilinear Coordinates

(iii)div v
Using the components of Vv obtained in (ii), we have

(iv)curl v
From the definition of the curl and Eq. (2D3.17) we have

(v)Components ofdiv T
Using the definition of the divergence of a tensor, Eq. (2C4.3), with the vector a equal to
the unit base vector e r gives

To evaluate the first term on the right-hand side, we note that

so that according to Eq. (2D3.18), with v r=T m v e=T^, 7^=

To evaluate the second term on the right-hand side of Eq. (2D3.20) we first use Eq. (2D3.17)
with v=e r to obtain