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Proving angular momentum is conserved

  1. Jan 11, 2009 #1
    1. The problem statement, all variables and given/known data
    A ball moves in a two-dimensional billiard comprising a horizontal frictionless table enclosed by two circular barriers of radii 2m and 1m and centred, respectively, at (x, y)=(0, 0) and (x, y)=(a, 0), where a<0.5m. The ball undergoes specular reflection at each barrier. Prove that the ball's angular momentum is conserved when a=0.


    2. Relevant equations
    Poisson brackets


    3. The attempt at a solution
    I know that I have to bring poisson brackets into this, since it basically comes down to showing constants of motion, although I don't know what I need to use poisson brackets on. I think that I need to consider [itex]L^2[/itex] and the hamiltonian of the system, but I'm not entirely sure how to build the boundary conditions (e.g. specular reflection off the boundary walls) into the hamiltonian.
     
  2. jcsd
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