Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems

Hiroaki Yoshimura*, Jerrold E. Marsden

*この研究の対応する著者

研究成果: Conference contribution

10 被引用数 (Scopus)

抄録

This paper begins by recalling how a constraint distribution on a configuration manifold induces a Dirac structure together with an implicit Lagrangian system, a construction that is valid even for degenerate Lagrangians. In such degenerate cases, it is shown in this paper that an implicit Hamiltonian system can be constructed by using a generalized Legendre transformation, where the primary constraints are incorporated into a generalized Hamiltonian on the Pontryagin bundle. Some examples of degenerate Lagrangians for L-C circuits, nonholonomic systems, and point vortices illustrate the theory.

本文言語English
ホスト出版物のタイトルLagrangian and Hamiltonian Methods for Nonlinear Control 2006 - Proceedings from the 3rd IFAC Workshop
出版社Springer Verlag
ページ233-247
ページ数15
ISBN(印刷版)3540738894, 9783540738893
DOI
出版ステータスPublished - 2007
イベント3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006 - Nagoya, Japan
継続期間: 2006 7月 192006 7月 21

出版物シリーズ

名前Lecture Notes in Control and Information Sciences
366 LNCIS
ISSN(印刷版)0170-8643

Conference

Conference3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006
国/地域Japan
CityNagoya
Period06/7/1906/7/21

ASJC Scopus subject areas

  • 図書館情報学

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