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About integrable systems

  1. Nov 21, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm asked to prove that if the Hamilton Jacobi equation is separable in certain coordinates then the system is integrable, that is, there exist [tex] n[/tex] integrals of motion in involution.


    2. Relevant equations



    3. The attempt at a solution

    If the H-J equation

    [tex]
    H\left(q^i,\frac{\partial G}{\partial q^i}\right)=-\frac{\partial G}{\partial t}
    [/tex]

    is separable then it means that

    [tex]
    G=T(t)+Q_1(q^1)+\ldots+Q_n(q^n)
    [/tex]

    At first I thought that [tex]Q_i [/tex] would be the integrals of motion but later I realized that is not the case. What can I do next?

    Thanks
     
  2. jcsd
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