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Lagrangian -> Equation of motion derivation

  1. Dec 25, 2011 #1
    1. The problem statement, all variables and given/known data
    I teach myself classical mechanics from David Tong
    http://www.damtp.cam.ac.uk/user/tong/dynamics.html
    From the homework set
    I should verify that the Lagrangian

    L=[itex]\frac{1}{12}m^{2}\dot{x}^{4}+m\dot{x}^{2}V-V^{2}[/itex]

    Yields the same equations as the mere L=[itex]\frac{1}{2}m\dot{x}^{2}-V[/itex]



    2. Relevant equations

    Lagranges equation of motion

    3. The attempt at a solution

    This seems kinda trivial exercise, straightforward derivative computation yields

    something like
    [itex]m\dot{x}^{2}\left(\frac{\partial V}{\partial x}-m\ddot{x}\right)-2V\left(\frac{\partial V}{\partial x}+m\ddot{x}\right)=0[/itex]

    which should somehow factor out and give simple equation.

    Still, it does not seem to...

    Could anyone help with this one?
     
  2. jcsd
  3. Dec 25, 2011 #2

    vela

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    I think you just made a sign error somewhere. Recheck your algebra.
     
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