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Question regarding generalized momentum Pk, and its independence from gen. coord. Qk

  1. Aug 16, 2012 #1
    Hi Physicsforums

    I am re-learning classical mechanics and having a tough time dealing with a certain line from Thornton/Marion. On page 269 (5th ed), a little after introducing Hamiltonian dynamics and the canonical conjugate equations of motion, the author says: "the qk and the pk are independent, whereas the qk and the [itex]\dot{q}[/itex]k are not". The context is describing the advantages of using Hamiltonian dynamics over Lagrangian

    In my mind, I see pk = m[itex]\dot{q}[/itex]k. If this is the case, I don't see how the author's statement stands.

    Thank you for your time
  2. jcsd
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