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luisgml_2000
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Homework Statement
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.
Homework Equations
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?