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Hamilton's equations of motion

  1. Oct 14, 2012 #1
    Having a bit of trouble with this question, if anyone could help?

    For the following questions we assume the Hamiltonian to
    be of the generic form
    H(r, p) = T(p) + V (r) = p2/2m+ V(r)
    where T(p) and V (r) denote kinetic and potential energies, respectively.
    Find Hamilton's equations of motion for a general quadratic potential V (r) = [(r,Ar)]/2
    A = AT , a symmetric 3-by-3 matrix.
    Which force do you obtain?
    Is this force conservative?

    Thanks!
     
  2. jcsd
  3. Oct 14, 2012 #2

    tiny-tim

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    welcome to pf!

    hi physics-?! welcome to pf! :wink:

    show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
     
  4. Oct 14, 2012 #3
    Well if i'm honest I don't really know where to begin!
    I am having trouble understanding it.
    Sorry that's not much use to you!
     
  5. Oct 14, 2012 #4

    tiny-tim

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    if A was diagonal, (r,Ar) would be ax2 + by2 + cz2

    the off-diagonal elements add some xy and yz and zx to that
     
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