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

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 \{\lambda + \mu cos [ \nu ( 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 .