Invariant Lagrangians, mechanical connections and the Lagrange ndaish Poincaré equations

"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 with 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."http://deepblue.lib.umich.edu/bitstream/2027.42/64235/1/a8_34_344015.pd