Averaging using elliptic functions: Approximation of limit cycles
From MaRDI portal
Publication:913072
DOI10.1007/BF01176982zbMath0699.34032OpenAlexW1986177202MaRDI QIDQ913072
Vincent T. Coppola, Richard H. Rand
Publication date: 1990
Published in: Acta Mechanica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01176982
small parameterlimit cyclesmethod of averagingelliptic functionsJacobian elliptic functionsautonomous systemMACSYMA
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Averaging method for ordinary differential equations (34C29) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)
Related Items (29)
Higher-Order Complex Periodic Motions in a Nonlinear, Electromagnetically Tuned Mass Damper System ⋮ Predicting homoclinic and heteroclinic bifurcation of generalized Duffing-harmonic-van der Pol oscillator ⋮ Transitions from strongly to weakly-nonlinear dynamics in a class of exactly solvable oscillators and nonlinear beat phenomena ⋮ Elliptic balance solution of two-degree-of-freedom, undamped, forced systems with cubic nonlinearity ⋮ Two models for the parametric forcing of a nonlinear oscillator ⋮ Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by the hyperbolic perturbation method ⋮ Modelling and analysis of the nonlinear string-mass structure of the vibration absorber ⋮ Approximate solution of a time-dependent differential equation ⋮ A new method for the periodic solution of strongly nonlinear systems ⋮ Period-m Motions to Chaos in a Periodically Forced, Duffing Oscillator with a Time-Delayed Displacement ⋮ Periodic Behavior of Maps Obtained by Small Perturbations of Smooth Skew Products ⋮ Dynamics of three coupled limit cycle oscillators with vastly different frequencies ⋮ Analytical approximations to a generalized forced damped complex Duffing oscillator: multiple scales method and KBM approach ⋮ Approximations for period-1 rotation of vertically and horizontally excited parametric pendulum ⋮ Homotopy-perturbation method for pure nonlinear differential equation ⋮ A quantitative stability and bifurcation analysis of the generalized Duffing oscillator with strong nonlinearity ⋮ ANALYTICAL DYNAMICS OF PERIOD-m FLOWS AND CHAOS IN NONLINEAR SYSTEMS ⋮ Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type ⋮ Averaging oscillations with small fractional damping and delayed terms ⋮ On a new criterion for evaluating the stability of the limit cycles of perturbed duffing oscillators ⋮ THE DYNAMICS OF SYSTEMS OF COMPLEX NONLINEAR OSCILLATORS: A REVIEW ⋮ On Periodic Motions in a Time-Delayed, Quadratic Nonlinear Oscillator with Excitation ⋮ Periodic Motions to Chaos in Pendulum ⋮ On The Elliptic Balance Method ⋮ ASYMMETRIC PERIODIC MOTIONS WITH CHAOS IN A SOFTENING DUFFING OSCILLATOR ⋮ Prediction of homoclinic bifurcation: the elliptic averaging method ⋮ Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems ⋮ Period-3 motions to chaos in an inverted pendulum with a periodic base movement ⋮ Homoclinic bifurcation of strongly nonlinear oscillators by frequency-incremental method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Perturbation methods, bifurcation theory and computer algebra
- Perturbation methods in applied mathematics
- Averaging method for the solution of non-linear differential equations with periodic non-harmonic solutions
- Construction of approximate analytical solutions to a new class of non-linear oscillator equations
- Generalized Fourier series and limit cycles of generalized van der Pol oscillators
- Asymptotic solutions of nonlinear second order differential equations with variable coefficients
- Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators
- Electron motion in a wave of slowly varying amplitude
- A generalization of the method of harmonic balance
- Averaging methods in nonlinear dynamical systems
This page was built for publication: Averaging using elliptic functions: Approximation of limit cycles
