Kinetic Energy in Spherical Coordinates? (For the Lagrangian)

[pergradus]

I'm doing a Lagrangian problem in spherical coordinates, and I was unsure how to express the kinetic energy, so I looked it up and wiki states it should be this:

http://en.wikipedia.org/wiki/Lagrangian#In_the_spherical_coordinate_system

Which would give me the correct answer, but I'm unsure how one would derive that expression. Can someone explain it? You don't necessarily have to do all the work out, just an explanation of the steps would help greatly.

Thanks.

 

[Bill_K]

The conversion to spherical coordinates is

x = r sin θ cos φ
y = r sin θ sin φ
z = r cos θ

Plug these into the expression for kinetic energy: T = ½m(x^·2 + y^·2 + z^·2) and simplify.

 

[pergradus]

Ok I'll try it! That looks simple... doh!