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.
Variational Problems with Symmetries : A Pfaffian System Approach / P. Morando, S. Sammarco. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - 120:1(2012 Aug), pp. 255-274. [10.1007/s10440-012-9720-4]
Variational Problems with Symmetries : A Pfaffian System Approach
P. MorandoPrimo
;S. SammarcoUltimo
2012
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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