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Lagrangian for simple pendulum

  1. Nov 2, 2006 #1
    Find the Lagrangian for a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant frequency [itex]\omega[/itex] in a uniform gravitational field.

    Let 'l' be the length of the pendulum string. Using plane polar coordinates:
    Let T be the KE of the pendulum.
    [tex]T = {1\over 2}m \left(\dot {r}^2 + r^2\dot{\theta}^2\right)[/tex]
    Let V be the PE.
    [tex]V = -mgr\cos \theta[/tex]
    r = l = constant
    I am wondering how to add the angular velocity [itex]\omega[/itex] to the equation of motion. Need help here.
  2. jcsd
  3. Nov 2, 2006 #2
    how is omega related to theta?
  4. Nov 2, 2006 #3


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    Homework Helper

    As with your other problem, You need to pick a pair of coordinates. A pair of angles looks good here also.
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