Page 80 - Introduction to Continuum Mechanics

PartD Spherical Coordinates 65

Substituting this equation into Eq. (2D3.11) and rearranging terms we have

But from Eq. (2D3.10) we have,

and from calculus we have

Thus, using Eqs. (2D3.15) and Eqs. (2D3.4), Eq. ( 2D3.14) becomes

In order that Eqs. (2D3.13) and (2D3.16) agree for all increments dr, dO, d<p, we have

which we display in matrix form as