Lagrangian block diagonalization (Q1183219)

J. C. Simo in collaboration with the author and others [\textit{J. C. Simo, D. Lewis}, and \textit{J. E. Marsden}, Arch. Ration. Mech. Anal. 115, No. 1, 15-59 (1991); \textit{J. C. Simo, T. A. Posbergh} and \textit{J. E. Marsden}, Arch. Ration. Mech. Anal. 115, No. 1, 60-100 (1991)] developed a reduced energy-momentum method in order to study the stability of steady motions of Hamiltonian and Lagrangian systems with symmetry. The original method was applicable only to simple mechanical systems. In the present work the author extends the method to a more general class of conservative systems including those on which the symmetry group does not act freely. A number of simple examples, including natural mechanical systems, are used to illustrate the block diagonalization procedure used in the work.