Page 76 - Introduction to Continuum Mechanics

Part D Cylindrical Coordinates 61

In a similar manner, (see Prob. 2D1), one can derive

2D2 Cylindrical Coordinates
In cylindrical coordinates, see Fig. 2D.3, the position of a point P is determined by (r,6^)
where r and 6 determine the position of the vertical projection of the point P on the xy plane
(the point P' in the figure) and the coordinate z determines the height of the point P from the
xy plane. In other words, the cylindrical coordinates is comprised of polar coordinates (r,B) in
the xy plane plus a coordinate z perpendicular to the xy plane.

Fig.2D3

We shall denote the position vector of P by R, rather than r, to avoid the possible confusion
between the position vector R and the coordinate r (which is a radial distance in the xy plane).
The unit vector e r and e# are on the xy plane and it is clear from the above figure that