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I am trying to understand how to use Liouville integrability to solve a question, but I could not understand how to calculate the functions $H_1,\ldots,H_n$ which are functionally independent (their wedge product is not equal to zero) and $\{H_j,H_k\}=0$ for all $j,k$ (the bracket is Poisson bracket) and each one is equal to the Hamiltonian

Frederik vom Ende
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Maria
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Apr 17 '23 at 14:29
  • Well, they are the constants of motion, of course. But you will need to provide a lot more detail if you want to get a sensible answer. What exactly is your question? What is the problem that you're working on? What's the context where you encountered this problem? Etc. – Hans Lundmark Apr 17 '23 at 14:52
  • I am trying to understand for the Hamiltonian H= \sum1/2 p^2_j - g^2\sum 1/(q^j-q^k)^2, j=1,...,n and j\leq k ,how we get H_1= trL , H_j=1/j tr L^j where L is matrix with diagonal p1,...,pn and the entries above the diagonal ig/(q^j-q^k) – Maria Apr 17 '23 at 15:10
  • Please edit the question to include the relevant details, and use MathJax to make the formulas readable. – Hans Lundmark Apr 17 '23 at 19:22

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