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k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations

  • Angel M. Rey
  • Narciso Román-RoyEmail author
  • Modesto Salgado
  • Silvia Vilariño
Article

Abstract

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner–Rusk formulation on classical mechanics.

Keywords

K-cosymplectic manifolds Classical field theory Lagrangian formalism Hamiltonian formalism 

Mathematics Subject Classifications (2010)

70S05 53D05 53Z05 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Angel M. Rey
    • 1
  • Narciso Román-Roy
    • 2
    Email author
  • Modesto Salgado
    • 1
  • Silvia Vilariño
    • 3
  1. 1.Departamento de Xeometría e Topoloxía, Facultade de MatemáticasUniversidade de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Departamento de Matemática Aplicada IVTechnical University of CataloniaBarcelonaSpain
  3. 3.Centro Universitario de La Defensa. Academia General Militar, Carretera de HuescaZaragozaSpain

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