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Canonical transformation

  1. Oct 16, 2012 #1
    There's a part in my book that I don't understand. I have attached the part and it is basically about how to transform from a set of conjugate variables (q,p) to another (Q,P) while preserving the hamilton equations of motion. I dont understand what he means by q,Q being separately independent. Don't we seek transformation where Q is a function of q. Maybe I'm just not into what he means by this independency.
     

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  2. jcsd
  3. Oct 16, 2012 #2

    dextercioby

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    It's true, but he means that for F q and Q are variables, so that there's no linear dependence between their time derivatives. Such a linear dependence would spoil his argument.
     
  4. Oct 16, 2012 #3
    Please elaborate. If Q = Q(q,p,t) how is its time derivative independent of q? :(
     
  5. Oct 17, 2012 #4

    dextercioby

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    Well, what is said was that there is no linear dependence between [itex] \displaystyle{\dot{Q}} [/itex] and [itex] \displaystyle{\dot{q}} [/itex].
     
  6. Oct 17, 2012 #5
    but dQ/dt = [itex]\partial[/itex]Q/[itex]\partial[/itex]q dq/dt + .....
    How is that not a relation between them?
     
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