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Lagrange equations on a sphere

  1. Oct 17, 2007 #1
    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:

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

    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. jcsd
  3. Oct 23, 2007 #2
    if you expressed x,y and Z in cordonnée spherical I believe that correct
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