Reduction of Exterior Differential Systems for ordinary variational problems

This paper deals with the reduction of ordinary variational problems with Abelian and non Abelian symmetry group. It differs from the existing results on geometric reduction in the approach that is completely Lagrangian and based on Exterior Differential Systems. In this setting two procedures of reduction come out naturally: the first one is the Lagrangian analogue of the Marsden-Weinstein reduction holding in the symplectic case; the other one, especially in the non Abelian case, comes out naturally in our setting.