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

DOI10.1063/1.4731481zbMath1277.70023arXiv1207.2814OpenAlexW2062869501MaRDI QIDQ2865512

Hiroaki Yoshimura, Melvin Leok, Joris Vankerschaver

Publication date: 29 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.2814

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Poisson manifolds; Poisson groupoids and algebroids (53D17) Hamilton's principle (70H25) Electromagnetic theory (general) (78A25) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Lagrange's equations (70H03)

Related Items (11)

Multisymplectic Hamiltonian variational integrators ⋮ Multisymplectic Geometry and Lie Groupoids ⋮ Clebsch variational principles in field theories and singular solutions of covariant EPDiff equations ⋮ Poisson-Poincaré reduction for field theories ⋮ Geometric methods for adjoint systems ⋮ Dirac structures in nonequilibrium thermodynamics for simple open systems ⋮ Routh reduction and Cartan mechanics ⋮ On the geometry of multi-Dirac structures and Gerstenhaber algebras ⋮ Tensor products of Dirac structures and interconnection in Lagrangian mechanics ⋮ Variational discretizations of gauge field theories using group-equivariant interpolation ⋮ Dirac Structures and Variational Formulation of Thermodynamics for Open Systems

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