2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168165We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory.22 pages, to appear in J. Phys. A: Math. Theor., D2HFest special issueDifferential GeometryMathematical Physics34A26; 37J15; 53C05; 70H03text