Page 72 - Introduction to Continuum Mechanics

Part D Polar Coordinates 57

Part D Curvilinear Coordinates

2D1 Polar Coordinates

In this section, the invariant definitions of Vf, Vv, diw and divT will be utilized in order to
determine their components in plane polar coordinates.
Let r,0 denote, see Fig. 2D.1, plane polar coordinates such that

Fig. 2D.1

The unit base vectors e,. and e# can be expressed in terms of the Cartesian base vectors
ei and 62 as:

These unit base vectors vary in direction as 0 changes. In fact, from Eqs. (2Dl.la) and
(2Dl.lb), it is easily derived that