N particles on a line with inverse-square repulsion: V = Σ g²/(xᵢ−xⱼ)². An exactly integrable Hamiltonian system — the Lax matrix L(λ) yields N conserved quantities.
Trajectories shown in phase space (position × velocity). Energy H = ½Σpᵢ² + Σᵢ＜ⱼ g²/(xᵢ−xⱼ)² is conserved.