New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

DOI10.1142/s0219887820500905arXiv1907.02947OpenAlexW3105520661MaRDI QIDQ6199420

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

Publication date: 23 February 2024

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.02947

zbMATH Keywords

symmetryHamiltonian formalismcontact manifoldLagrangian formalismdissipative systemdissipation law

Mathematics Subject Classification ID

Hamilton's equations (70H05) Contact manifolds (general theory) (53D10) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Lagrange's equations (70H03) Contact systems (37J55)

Related Items (15)

Orbital dynamics on invariant sets of contact Hamiltonian systems ⋮ Generalized virial theorem for contact Hamiltonian systems ⋮ Scaling symmetries, contact reduction and Poincaré’s dream ⋮ Unified Lagrangian‐Hamiltonian Formalism for Contact Systems ⋮ The flow method for the Baker-Campbell-Hausdorff formula: exact results ⋮ 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 ⋮ Bregman dynamics, contact transformations and convex optimization ⋮ On the geometry of discrete contact mechanics ⋮ A \(K\)-contact Lagrangian formulation for nonconservative field theories ⋮ A geometric approach to contact Hamiltonians and contact Hamilton–Jacobi theory ⋮ On locally conformally cosymplectic Hamiltonian dynamics and Hamilton–Jacobi theory ⋮ Multicontact formulation for non-conservative field theories

Cites Work

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• A contact geometry framework for field theories with dissipation
• Infinitesimal symmetries in contact Hamiltonian systems
• Methods of Differential Geometry in Classical Field Theories
• Applications of Contact Geometry and Topology in Physics
• Nonstandard Hamiltonian structures of the Liénard equation and contact geometry
• An Introduction to Contact Topology

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