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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