A \(K\)-contact Lagrangian formulation for nonconservative field theories

DOI10.1016/S0034-4877(21)00041-0zbMath1487.70095arXiv2002.10458MaRDI QIDQ2040737

Xavier Rivas, Xavier Gràcia, Jordi Gaset, Miguel C. Muñoz-Lecanda, Narciso Román-Roy

Publication date: 14 July 2021

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.10458

zbMATH Keywords

dissipationcontact structureLagrangian systemfield theory\(k\)-symplectic structure\(k\)-contact structure

Mathematics Subject Classification ID

General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Contact manifolds (general theory) (53D10) 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) Symmetries and conservation laws in mechanics of particles and systems (70S10) PDEs on manifolds (35R01)

Related Items (13)

When action is not least for systems with action-dependent Lagrangians ⋮ Nonautonomous k-contact field theories ⋮ Skinner-Rusk formalism for \(k\)-contact systems ⋮ Symmetries, Conservation and Dissipation in Time‐Dependent Contact Systems ⋮ Time-dependent contact mechanics ⋮ Lagrangian-Hamiltonian formalism for cocontact systems ⋮ A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian ⋮ Contact Lie systems: theory and applications ⋮ Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems ⋮ Optimal control, contact dynamics and Herglotz variational problem ⋮ Constrained Lagrangian dissipative contact dynamics ⋮ Contact Lagrangian systems subject to impulsive constraints ⋮ Multicontact formulation for non-conservative field theories

Cites Work

• On the \(k\)-symplectic, \(k\)-cosymplectic and multisymplectic formalisms of classical field theories
• Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories
• p-almost tangent structures
• On the multisymplectic formalism for first order field theories
• Fibre derivatives: Some applications to singular Lagrangians
• Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior
• Contact manifolds and dissipation, classical and quantum
• A contact geometry framework for field theories with dissipation
• Constraint algorithm for singular field theories in the \(k\)-cosymplectic framework
• Contact Hamiltonian mechanics
• Geometry of Lagrangian First-order Classical Field Theories
• Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics
• Introduction to Smooth Manifolds
• Günther’s formalism (k-symplectic formalism) in classical field theory: Skinner–Rusk approach and the evolution operator
• Symmetries and infinitesimal symmetries of singular differential equations
• k-symplectic structures
• Applications of Contact Geometry and Topology in Physics
• Contact Hamiltonian systems
• Nonstandard Hamiltonian structures of the Liénard equation and contact geometry
• Contact geometry and thermodynamics
• Partial Stabilization of Input-Output Contact Systems on a Legendre Submanifold
• Cosymplectic and contact structures for time-dependent and dissipative Hamiltonian systems
• An Introduction to Contact Topology
• SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY
• Singular Lagrangians and precontact Hamiltonian systems
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• Unnamed Item
• Unnamed Item

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