The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories

J. Vankerschaver*, H. Yoshimura, M. Leok

*この研究の対応する著者

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We introduce a variational principle for field theories, referred to as the Hamilton-Pontryagin principlewe show that the resulting field equations are the Euler-Lagrange equations in implicit form. Second, we introduce multi-Dirac structures as a graded analog of standard Dirac structureswe show that the graph of a multisymplectic form determines a multi-Dirac structure. We then discuss the role of multi-Dirac structures in field theory by showing that the implicit Euler-Lagrange equations for fields obtained from the Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac structures. Finally, we show a number of illustrative examples, including time-dependent mechanics, nonlinear scalar fields, Maxwell's equationselastostatics.

本文言語English
論文番号072903
ジャーナルJournal of Mathematical Physics
53
7
DOI
出版ステータスPublished - 2012 7 12

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

フィンガープリント

「The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル