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Derivation of Momentum as a Constant of motiion

  1. Sep 30, 2008 #1
    Following is the question.

    Using Hamilton’s equations of motion for a set on N interacting particles demonstrate that total linear momentum (P = Sigma pi, i : 1 to N) is a constant of motion. Assume the particles interact via a potential of the form: V({ri}).

    I am having a hard time figuring out the method to start the problem with. Do i start with the Hamiltonian H({ri}{pi}) = V({ri}) + Sigma(pi*t^2/2mi) where i goes from 1 to 3N.

    Then i take the time derivitive of the the Hamiltonian to end with the conservation of energy. But i do not understand how i can say that the linear momentum is conserved. Please help me.
  2. jcsd
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