Algebraic and Geometric Structure of the Integrable Models recently Proposed by Calogero

Abstract

We show that the integrability of the dynamical system recently proposed by Calogero and characterized by the Hamiltonian $ H = \sum_{j,k}^{N} p_j p_k \{λ+ μcos [ ν( q_j - q_k)] \} $ is due to a simple algebraic structure . It is shown that the integrals of motion are related to the Casimiar invariants of of the $su(1,1)$ algebra. Our method shows clearly how these types of systems can be generalized .