Nonstandard Hamiltonian structures of the Liénard equation and contact geometry

DOI10.1142/S0219887819400012zbMath1421.70030OpenAlexW2895951370MaRDI QIDQ5233075

José F. Cariñena, Partha Guha

Publication date: 13 September 2019

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

Full work available at URL: https://doi.org/10.1142/s0219887819400012

zbMATH Keywords

contact structureReeb vector fieldnonstandard Hamiltoniandeformed Lagrangian

Mathematics Subject Classification ID

Hamilton's equations (70H05) Applications of differential geometry to physics (53Z05) Contact manifolds (general theory) (53D10) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrange's equations (70H03)

Related Items (14)

Nonequilibrium thermodynamic process with hysteresis and metastable states—A contact Hamiltonian with unstable and stable segments of a Legendre submanifold ⋮ Nonautonomous k-contact field theories ⋮ Higher-order contact mechanics ⋮ Skinner-Rusk formalism for \(k\)-contact systems ⋮ Generalized virial theorem for contact Hamiltonian systems ⋮ Unified Lagrangian‐Hamiltonian Formalism for Contact Systems ⋮ New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries ⋮ Non-standard magnetohydrodynamics equations and their implications in sunspots ⋮ Darboux first integrals and linearizability of quadratic-quintic Duffing-van der Pol oscillators ⋮ A \(K\)-contact Lagrangian formulation for nonconservative field theories ⋮ Constrained Lagrangian dissipative contact dynamics ⋮ On a new generalized local fractal derivative operator ⋮ Jacobi multipliers and Hamel’s formalism ⋮ Multicontact formulation for non-conservative field theories

Cites Work

• Unnamed Item
• Unnamed Item
• On the criteria for integrability of the Liénard equation
• Geometric approach to dynamics obtained by deformation of Lagrangians
• Geometric approach to dynamics obtained by deformation of time-dependent Lagrangians
• Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations
• A class of exact solutions of the Liénard-type ordinary nonlinear differential equation
• Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation
• A geometric approach to integrability of Abel differential equations
• On the connection of the quadratic Liénard equation with an equation for the elliptic functions
• New exact general solutions of Abel equation of the second kind
• Quasi-Lie families, schemes, invariants and their applications to Abel equations
• Contact Hamiltonian mechanics
• A general equation for relaxation oscillations
• A Brief Introduction to Symplectic and Contact Manifolds
• Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier
• Tangent bundle geometry Lagrangian dynamics
• Non-Noether constants of motion
• Equivalent Lagrangians: Multidimensional case
• On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamics
• Geometry from Dynamics, Classical and Quantum
• Jacobi multipliers, non-local symmetries, and nonlinear oscillators
• On quantized Liénard oscillator and momentum dependent mass
• An Analytic Technique for the Solutions of Nonlinear Oscillators with Damping Using the Abel Equation

This page was built for publication: Nonstandard Hamiltonian structures of the Liénard equation and contact geometry