Multicontact formulation for non-conservative field theories

Abstract

A new geometric framework is developed to describe non-conservative classical field theories, which is based on multisymplectic and contact geometries. Assuming certain additional conditions and using the forms that define this multicontact structure, as well as other geometric elements that are derived from them, we can introduce variational field equations in the multicontact manifolds. These equations are stated using different geometric tools; namely, sections, multivector fields and Ehresmann connections in fiber bundles. Then, this framework can be adapted to the jet bundle description of classical field theories and the field equations are stated both in the Lagrangian and the Hamiltonian formalisms, which are discussed in the regular and the singular cases.

44 pp

References in corpus (5)

• A Geometric Hamilton-Jacobi Theory for Classical Field Theories
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Contact Lie systems
• A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian
• A new canonical affine BRACKET formulation of Hamiltonian Classical Field theories of first order

Cited by in corpus (12)

• Symmetries, conservation and dissipation in time-dependent contact systems
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Contact Lie systems
• Nonautonomous k-contact field theories
• The Herglotz variational principle for dissipative field theories
• A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian
• Practical Introduction to Action-Dependent Field Theories
• Coisotropic reduction in Multisymplectic Geometry
• Graded Poisson and Graded Dirac structures
• Contact Lie systems on Riemannian and Lorentzian spaces: from scaling symmetries to curvature-dependent reductions
• A Hamiltonian formalism for general variational problems, with applications to first order gravity with basis
• Brackets in multicontact geometry and multisymplectization