Order and Chaos in a Discrete Duffing Oscillator: Implications on Numerical Integration

DOI10.1115/1.3176039zbMath0686.70009OpenAlexW1990025462MaRDI QIDQ4205101

Per G. Reinhall, T. K. Caughey, Duane Storti

Publication date: 1989

Published in: Journal of Applied Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1115/1.3176039

zbMATH Keywords

Jacobi elliptic functionsnumerical integration schemescubic stiffness nonlinearitydiscrete Duffing equationtwo-dimensional mappings

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Random vibrations in mechanics of particles and systems (70L05)

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Influence of the Integration Steps on the Results of Numerical Simulations for a System with Friction ⋮ Instability, chaos, and growth and decay of energy of time‐stepping schemes for non‐linear dynamic equations ⋮ Perpetual points and periodic perpetual loci in maps ⋮ Detecting the unstable periodic orbits of chaotic nonautonomous systems with an approximate global Poincaré map ⋮ Chaos in mechanical systems -- a review ⋮ Extended framework of Hamilton's principle applied to Duffing oscillation ⋮ Spectral element methods for nonlinear temporal dynamical systems ⋮ Discrete dynamics of implicit time integration schemes for a dissipative system ⋮ Duffing Oscillator and Elliptic Curve Cryptography ⋮ Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling ⋮ Non-linear dynamics versus chaotic motion for MDOF structural systems.

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