Page 78 - Introduction to Continuum Mechanics
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Part D Spherical Coordinates 63
r
We note that in dyadic notation, divT is written as V-T, so that (div T)^ = (V-T)^ etc.
2D3 Spherical Coordinates
In Fig. 2D.4a, we show the spherical coordinates (r,0 t<j>) of a general point P. In this figure,
e-.efl and e* are unit vectors in the direction of increasing r.Ojtb respectively.
Fig. 2D.4
The position vector for the point P can be written as
where r is the magnitude of the vector r. Thus,
To evaluate de n we note from Fig. 2D.4b that
where e/ is the unit vector in the r' (OE) direction (r' is in the xy plane). Thus,
de r = -sm&dOe z+cosOdOe r' + sinftfe/ = d0(-sin0e z+cos0e/ )+sin0de r'
But, just like in polar coordinates, due to d<j>, de r' =(l)d<f)e tj >, therefore,
