AN INTEGRABLE 3-PARTICLE SYSTEM

A study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized (dynamical or hidden) symmetries. Two Lagrangians are considered, both obtained by modifying the Toda Lagrangian. First a two-particle system is studied and then the results are generalized to a three-particle system. It is shown that in both cases the Lagrangians possess nonlinear constants of motion in involution and, thus, they are integrable.