Asymptotically stable non-falling solutions of the Kapitza-Whitney pendulum

DOI10.1007/S11012-023-01665-2arXiv2205.12057OpenAlexW4376646789MaRDI QIDQ6172059

I. Yu. Polekhin

Publication date: 18 July 2023

Published in: Meccanica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.12057

zbMATH Keywords

Poincaré methodnumerical continuation methodnon-autonomous Lyapunov systemperiodic non-falling solution existenceweak/large horizontal force

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Forced motions for nonlinear problems in mechanics (70K40) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Computational methods for problems pertaining to mechanics of particles and systems (70-08)

Cites Work

• The stability of the equilibrium of a pendulum for vertical oscillations of the point of suspension
• Stability properties of periodic solutions of a Duffing equation in the presence of lower and upper solutions.
• The method of averaging for the Kapitza-Whitney pendulum
• Parametric stability of a charged pendulum with an oscillating suspension point
• Existence and stability of periodic solutions of a Duffing equation by using a new maximum principle
• Parametric stability of a charged pendulum with oscillating suspension point
• Calculus of variations in the large, existence of trajectories in a domain with boundary, and Whitney's inverted pendulum problem
• N.N. Bogolyubov and non-linear mechanics
• The pendulum under vibrations revisited
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