Generalized Lagrangian dynamics and Noetherian symmetries

In this paper, the authors propose a generalization of the usual Lagrangian formulation of dynamics, suggested by the Souriau approach to analytical mechanics. It is a global formulation in which the Lagrangian is defined, in general, only locally. Some examples of generalized dynamics are given in this sense. The authors analyze in detail the Galilean invariant N-particle system and we also study the case of identical particles