Invariant Lagrangians , mechanical connections and the Lagrange - Poincaré equations
نویسنده
چکیده
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-Poincaré 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. Mathematics Subject Classification (2000). 34A26, 37J15, 53C05, 70H03.
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