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Example of integrable system

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data

    3 unit masses move around a unit circle. Between them there is a repulsive force that decreases with the angle between the particles as

    [tex]
    F_{ij}=\exp(-(\theta_i-\theta_j))
    [/tex]

    The problem is to find 3 conserved quantities in involution.

    2. Relevant equations



    3. The attempt at a solution

    From physical considerations we can see that both the total mechanical energy and the total angular momentum are integrals of motion, but I'm missing the 3rd one. Any idea?
     
  2. jcsd
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