Analytical solution of the damped Helmholtz-Duffing equation
From MaRDI portal
Publication:714596
DOI10.1016/J.AML.2012.06.030zbMath1259.34004OpenAlexW1981030281MaRDI QIDQ714596
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
asymmetric behaviorquadratic nonlinearitiesdamped Helmholtz-Duffing oscillatormixed-parity nonlinear oscillator
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
This page was built for publication: Analytical solution of the damped Helmholtz-Duffing equation
