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Poisson Brackets

  1. May 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Calculate the Poisson bracket [H, Lz] in Cartesian Coords. Transform your result to cylndrical coords to show that [H, Lz] = -dU/dphi (note: partial derivs), where U is the potential energy. Identify the equivalent result in the Lagrangian formulation

    2. Relevant equations



    3. The attempt at a solution
    I was able to do the first part easily enough, after a lot of math. I am having trouble figuring out what the question means by showing the equivalent result in Lagrangian formulation.

    The best I have been able to come up with is:
    L = 1/2*m*(r'^2 + r^2*(phi')^2) - U(r,phi,z)
    [tex]\frac{\partial L}{\partial \phi} = - \frac{\partial U}{\partial \phi} = L_z[/tex]
    where [tex]L_z[/tex] = angular momentum
    I don't think that is what the question is asking?
    So angular momentum is not conserved?

    Can anyone set me on the right path?
     
    Last edited: May 4, 2009
  2. jcsd
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