Analytical solution of the damped Helmholtz-Duffing equation

DOI10.1016/J.AML.2012.06.030zbMath1259.34004OpenAlexW1981030281MaRDI QIDQ714596

Alex Elías-Zúñiga

Publication date: 11 October 2012

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2012.06.030

zbMATH Keywords

asymmetric behaviorquadratic nonlinearitiesdamped Helmholtz-Duffing oscillatormixed-parity nonlinear oscillator

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (12)

Solution of the damped cubic-quintic Duffing oscillator by using Jacobi elliptic functions ⋮ A new exact solution of a damped quadratic non-linear oscillator ⋮ A new approach for modelling the damped Helmholtz oscillator: applications to plasma physics and electronic circuits ⋮ Structure-preserving algorithms with uniform error bound and long-time energy conservation for highly oscillatory Hamiltonian systems ⋮ A Spring–Beam System with Signorini’S Condition and the Normal Compliance Condition ⋮ A generalized Duffing equation with the Coulomb's friction law and Signorini-type contact conditions ⋮ The frequency estimation for non‐conservative nonlinear oscillation ⋮ Towards an analytic solution of rapid roll inflation with a quartic potential ⋮ Volume-preserving exponential integrators and their applications ⋮ Exact solutions for the quadratic mixed-parity Helmholtz-Duffing oscillator by bifurcation theory of dynamical systems ⋮ Analytic solution to the generalized complex Duffing equation and its application in soliton theory ⋮ The damping term makes the Smale-horseshoe heteroclinic chaotic motion easier

Cites Work

• Exact solution of the quadratic mixed-parity Helmholtz-Duffing oscillator
• Monotonous property of non-oscillations of the damped Duffing's equation
• Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method—I: The fundamental mode of isotropic plates
• Integrability and symmetries for the Helmholtz oscillator with friction
• New aspects of integrability of force-free Duffing–van der Pol oscillator and related nonlinear systems

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