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Foucault Pendulum - Lagrangian

  1. Oct 27, 2007 #1
    1. The problem statement, all variables and given/known data
    I should find the Lagrangian of a Foucault Pendulum in a coordinate system on the earth. That means L = T - V where T is the cinetic energy of the pendulum and V the potential energy.

    2. Relevant equations

    [tex]v' = v + [\omega, r][/tex]
    [,] denotes the cross product


    3. The attempt at a solution
    I write the potential energy as
    [tex]T = \frac{1}{2}mv'^2 = \frac{1}{2}m( (\dot{x}+ \dot{y} + \dot{z}) + \omega*sqrt(x^2+ y^2 + z^2)*sin(\phi))^2[/tex]

    where [tex]\phi[/tex] denotes the latitude.
    The potential energy is given by
    [tex]V = mgz[/tex]
    But when I solve this I get strange results. Does anyone see my problem. Thanks a lot for your help!
     
  2. jcsd
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