"A Solvable Hamiltonian System" Integrability and Action-Angle Variables
Abstract
We prove that the dynamical system charaterized by the Hamiltonian H = λ N ΣjN pj + μ Σj,kN (pj pk)1 2 \ cos [ ( qj - qk)] \ proposed and studied by Calogero [1,2] is equivalent to a system of non-interacting harmonic oscillators. We find the explicit form of the conserved currents which are in involution. We also find the action-angle variables and solve the initial value problem in simple form.
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