The pendulum under vibrations revisited

DOI10.1088/1361-6544/ABBE65zbMath1481.70083OpenAlexW3125820199MaRDI QIDQ5147946

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Publication date: 29 January 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/abbe65

zbMATH Keywords

stabilizationYoung measuresStephenson-Kapitza pendulumvibrational forcesviolent vibrations

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Singular perturbations for ordinary differential equations (34E15)

Related Items (2)

The spherical Kapitza-Whitney pendulum ⋮ Asymptotically stable non-falling solutions of the Kapitza-Whitney pendulum

Cites Work

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• Weak convergence and averaging for ODE
• On the existence of periodic motions of the excited inverted pendulum by elementary methods
• Geometry and physics of averaging with applications
• An extension of the Levi-Weckesser method to the stabilization of the inverted pendulum under gravity
• Stability of the Inverted Pendulum—A Topological Explanation
• Stabilization of the Inverted Linearized Pendulum by High Frequency Vibrations
• Geometrical aspects of rapid vibrations and rotations
• Slow observables of singularly perturbed differential equations
• GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS
• AVERAGING IN SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

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