Page 75 - Introduction to Continuum Mechanics

60 Curvilinear Coordinates

In matrix form,

(iii) diw
Using the components of W obtained in (ii), we have

(iv) curl v
From the definition that curlv= twice the dual vector of (Vv)i , we have

(v) Components o/div T
The definition of the divergence of a second-order tensor is

for an arbitrary vector a.

Take a=e n then, the above equation gives

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

so that according to Eq. (2D1.11), with v r = T m and VQ = T^

To evaluate the second term, we first use Eq. (2D1.10) to obtain Ve r In fact, since
e r = (I)e r+0e0, we have, with v r= 1 and v e=Q in Eq. (2D1.10),