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

Hiroaki Yoshimura; Jerrold E. Marsden

doi:10.1007/978-3-540-73890-9_18

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

基幹理工学部

研究成果: Conference contribution

11 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	https://doi.org/10.1007/978-3-540-73890-9_18
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 19 → 2006 7月 21

出版物シリーズ

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

Conference

Conference	3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006
国/地域	Japan
City	Nagoya
Period	06/7/19 → 06/7/21

ASJC Scopus subject areas

図書館情報学

文献へのアクセス

10.1007/978-3-540-73890-9_18

他のファイルとリンク

引用スタイル

Yoshimura, H., & Marsden, J. E. (2007). Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. In Lagrangian and Hamiltonian Methods for Nonlinear Control 2006 - Proceedings from the 3rd IFAC Workshop (pp. 233-247). (Lecture Notes in Control and Information Sciences; Vol. 366 LNCIS). Springer Verlag. https://doi.org/10.1007/978-3-540-73890-9_18

Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. / Yoshimura, Hiroaki; Marsden, Jerrold E.
Lagrangian and Hamiltonian Methods for Nonlinear Control 2006 - Proceedings from the 3rd IFAC Workshop. Springer Verlag, 2007. p. 233-247 (Lecture Notes in Control and Information Sciences; Vol. 366 LNCIS).

研究成果: Conference contribution

Yoshimura, H & Marsden, JE 2007, Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. in Lagrangian and Hamiltonian Methods for Nonlinear Control 2006 - Proceedings from the 3rd IFAC Workshop. Lecture Notes in Control and Information Sciences, vol. 366 LNCIS, Springer Verlag, pp. 233-247, 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, LHMNLC 2006, Nagoya, Japan, 06/7/19. https://doi.org/10.1007/978-3-540-73890-9_18

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AB - 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.

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

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出版物シリーズ

Conference

ASJC Scopus subject areas

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