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A connection‐theoretic approach to reduction of second‐order dynamical systems with symmetry

We deal with reduction of Lagrangian systems that are invariant under the action of the symmetry group. Unlike the bulk of the literature we do not rely on methods coming from the calculus of variations. Our method is based on the geometrical analysis of regular Lagrangian systems, where solutions of the Euler‐Lagrange equations are interpreted as integral curves of the associated second‐order differential equation field. In particular, we explain so‐called Lagrange‐Poincaré reduction [1] and Routh reduction [3] from the viewpoint of that vector field. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)