Velocity in spherical polar coordinates

[meteo student]

I am looking at this derivation of velocity in spherical polar coordinates and I am confused by the definition of r, theta and phi.
http://www.usna.edu/Users/math/rmm/SphericalCoordinates.pdf

I thought phi was the co latitude in the r,θ,∅ system and not the latitude. Of course the two are related through the equation 90 - colatitude.

Would this change the derivation ?

 

[BvU]

Hello weatherstudent,

It's a choice that looks convenient for looking at the world with its historically grown coordinnate system.
Derivation doesn't change, but you want to be careful bringing in equations from other disciplines; you'll have a minus sign here and there, or the range of $\phi$ may cause confusion.

Physicists and and mathematicians also have created their own booby traps by adapting different spherical coordinate systems, so why shouldn't meteorologists have yet another one !

 

[meteo student]

Thanks for that response and the welcome. :-)

I wasn't referring to the convenience. Would substituting latitude for colatitude not change the equation as well ?