Implicit Lagrange-Routh equations and Dirac reduction

Eduardo García-Toraño Andrés, Tom Mestdag*, Hiroaki Yoshimura

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonomic frame, and how these equations can be reduced. To do this, we keep the momentum constraint implicit throughout and we make use of a Routhian function defined on a certain submanifold of the Pontryagin bundle. Then, we show how the reduced implicit Lagrange-Routh equations can be described in the context of dynamical systems associated to Dirac structures, in which we fully utilize a symmetry reduction procedure for implicit Hamiltonian systems with symmetry.

本文言語English
ページ(範囲)291-304
ページ数14
ジャーナルJournal of Geometry and Physics
104
DOI
出版ステータスPublished - 2016 6月 1

ASJC Scopus subject areas

  • 数理物理学
  • 物理学および天文学(全般)
  • 幾何学とトポロジー

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