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Predict nature of motion from Lagrangian.

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m moves in 1D such that it has Lagrangian,

    [itex]L=\frac{m^{2}\dot{x}^{4}}{12}+m\dot{x}^{2}V(x)-V_{2}(x)[/itex]
    where V is some differentiable function of x.Find equation of motion and describe the nature of motion based on the equation.

    3. The attempt at a solution
    Equation of motion is,
    [itex]\frac{d}{dt}(\frac{m^{2}\dot{x}^{3}}{3}+2m\dot{x}V(x))-m\dot{x}^{2}\frac{%
    \partial V}{\partial x}+\frac{\partial V_{2}}{\partial x}=0[/itex]

    [itex]m^{2}\dot{x}^{2}\ddot{x}+2m\ddot{x}V(x)-m\dot{x}^{2}\frac{\partial V}{%
    \partial x}+\frac{\partial V_{2}}{\partial x}=0[/itex]

    How can i predict nature of motion from this?
    Thanks.
     
  2. jcsd
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