The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories
The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories
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DOI：
10.1063/1.4731481
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发表时间：
2012-07-01
影响因子：
1.3
通讯作者：
Leok, M.
中科院分区：
文献类型：
--
作者：
Vankerschaver, J.;Yoshimura, H.;Leok, M.
We introduce a variational principle for field theories, referred to as the Hamilton-Pontryagin principle, and we 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 structures, and we 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 equations, and elastostatics. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4731481]
