Time-dependent contact mechanics

DOI10.1007/s00605-022-01767-1zbMath1523.37071arXiv2205.09454OpenAlexW4296193942WikidataQ114228817 ScholiaQ114228817MaRDI QIDQ6101255

Jordi Gaset, Xavier Gràcia, Xavier Rivas, Miguel C. Muñoz-Lecanda, Manuel de León

Publication date: 20 June 2023

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.09454

zbMATH Keywords

dissipationcontact structureholonomic constraintsHamiltonian systemJacobi structuresingular Lagrangiantime-dependent system

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Applications of differential geometry to physics (53Z05) Contact manifolds (general theory) (53D10) Constrained dynamics, Dirac's theory of constraints (70H45) Contact systems (37J55) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (10)

When action is not least for systems with action-dependent Lagrangians ⋮ Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds ⋮ Nonautonomous k-contact field theories ⋮ Generalized virial theorem for contact Hamiltonian systems ⋮ Reductions: precontact versus presymplectic ⋮ A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian ⋮ Contact Lie systems: theory and applications ⋮ Bregman dynamics, contact transformations and convex optimization ⋮ A geometric approach to contact Hamiltonians and contact Hamilton–Jacobi theory ⋮ Multicontact formulation for non-conservative field theories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Le théorème de réduction de Marsden-Weinstein en géométrie cosymplectique et de contact. (The Marsden-Weinstein reduction theorem in cosymplectic and contact geometry)
• Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories
• Reduction of symplectic manifolds with symmetry
• Les variétés de Jacobi et leurs algèbres de Lie associees
• On the multisymplectic formalism for first order field theories
• Some geometric aspects of variational calculus in constrained systems
• 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
• Numerical integration in celestial mechanics: a case for contact geometry
• On the geometry of discrete contact mechanics
• A \(K\)-contact Lagrangian formulation for nonconservative field theories
• Contact Hamiltonian and Lagrangian systems with nonholonomic constraints
• Contact Hamiltonian mechanics
• Higher-order contact mechanics
• Skinner-Rusk formalism for \(k\)-contact systems
• Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics
• GEOMETRICAL SETTING OF TIME-DEPENDENT REGULAR SYSTEMS: ALTERNATIVE MODELS.
• Gradient vector fields on cosymplectic manifolds
• The constraint algorithm for time-dependent Lagrangians
• Singular Lagrangian Systems on Jet Bundles
• Legendre transformation and analytical mechanics: A geometric approach
• Generalized variational principle of Herglotz for several independent variables. First Noether-type theorem
• Constrained Lagrangian dissipative contact dynamics
• Contact geometry for simple thermodynamical systems with friction
• Contact Hamiltonian systems
• 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
• GEOMETRIC ASPECTS OF TIME-DEPENDENT SINGULAR DIFFERENTIAL EQUATIONS
• Contact variational integrators
• Singular Lagrangians and precontact Hamiltonian systems
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

This page was built for publication: Time-dependent contact mechanics