Lagrangian for simple pendulum

  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. how is omega related to theta?
  4. OlderDan

    OlderDan 3,029
    Science Advisor
    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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