# Lagrange equations on a sphere

1. Oct 17, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
A particle moves on the surface of a sphere. Write down the Lagrange equations.

2. Relevant equations

3. The attempt at a solution
So since it is a free particle, there is no V in the Lagrangian, correct?

So L = T and I can write:

$$L = 1/2 m (R^2 \cos^2 \phi \dot{ \theta}^2 + R^2 \dot{\theta}^2)$$

phi is the azimuthal angle and theta is the polar angle

Is that all correct? If so, I only need to plug that into the EL equations, right?

Last edited: Oct 17, 2007
2. Oct 23, 2007