# Example of integrable system

1. Nov 29, 2009

### luisgml_2000

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

$$F_{ij}=\exp(-(\theta_i-\theta_j))$$

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?