Periodic oscillations and attracting basins for a parametrically excited pendulum

DOI10.1080/02681119408806172zbMath0807.34056OpenAlexW2071717264MaRDI QIDQ4306567

Danilo Capecchi, Steven R. Bishop

Publication date: 19 September 1994

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02681119408806172

zbMATH Keywords

stabilityperiodic motionharmonic balance methodGalerkin techniqueparametrically excited pendulumnumerical studiesattracting basins

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Theoretical approximation of solutions to ordinary differential equations (34A45) Stability of solutions to ordinary differential equations (34D20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Parametric resonances for nonlinear problems in mechanics (70K28)

Related Items (9)

Approximations for period-1 rotation of vertically and horizontally excited parametric pendulum ⋮ Detection and Classification of Solutions for Systems Interacting by Soft Impacts with Sample-Based Method ⋮ Comparisons between the pendulum with varying length and the pendulum with oscillating support ⋮ Synchronous states of slowly rotating pendula ⋮ Chaotic behavior in a dissipative non-ideal periodically kicked rotator ⋮ Breaking the symmetry of the parametrically excited pendulum ⋮ Analytically bounded and numerically unbounded compound pendulum chaos ⋮ Period-3 motions to chaos in an inverted pendulum with a periodic base movement ⋮ The use of manifold tangencies to predict orbits, bifurcations and estimate escape in driven systems.

Cites Work

• Unnamed Item
• Periodic response of a class of hysteretic oscillators
• Accurate solutions and stability criterion for periodic oscillations in hysteretic systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Experiments on periodic and chaotic motions of a parametrically forced pendulum
• Subharmonic and homoclinic bifurcations in a parametrically forced pendulum
• Fast Galerkin method and its application to determine periodic solutions of nonlinear oscillators
• Experimental study of chaos in a driven pendulum
• Numerical computation of nonlinear forced oscillations by Galerkin's procedure
• An intrinsic method of harmonic analysis for non-linear oscillations (a perturbation technique)
• Construction of chaotic regions
• Periodic response and stability of hysteretic oscillators
• On a periodically forced, weakly damped pendulum. Part 3: Vertical forcing
• Limit Cycle Oscillations of Parametrically Excited Second-Order Nonlinear Systems

This page was built for publication: Periodic oscillations and attracting basins for a parametrically excited pendulum