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2.6 Spherical Coordinates

Spherical coordinates uses a radial variable r, , a "polar angle" which measures the angle between r and k, and polar coordinates as before in the xy plane, except now .

(we also have, ; in other words our old r obeys )

We can now express r, v and a in spherical coordinates:

with

We now have two angular directions: as in polar coordinates we have

and now we have

and can deduce

We may therefore perform the differentiations to obtain

 

Spherical - cartesian  coordinates converter