Abstract
Reduction methods for completely integrable Pfaffian Systems with symmetry are applied to variational problems, providing analogues of the Arnold–Liouville Theorem and Marsden–Weinstein reduction in the Lagrangian setting. A generalization of the Mishchenko–Fomenko Theorem for non Abelian integrability is given in terms of solvable structures.
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Morando, P., Sammarco, S. Variational Problems with Symmetries: A Pfaffian System Approach. Acta Appl Math 120, 255–274 (2012). https://doi.org/10.1007/s10440-012-9720-4
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DOI: https://doi.org/10.1007/s10440-012-9720-4