  We 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.
