Abstract
The properties of some three-particle systems are studied using as an approach the theory of generalized or hidden symmetries. It is proven that the existence of a family that possesses, in addition to the Energy function, two nonlinear constants of motion in involution. This family of integrable systems is obtained by considering deformations of the Lagrangian of the Calogero–Moser system. Finally, the generalization of the results to the general case of n particles is discussed.
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