The pendulum under vibrations revisited

A simple intuitive physical explanation is offered, of the stability of the inverted pendulum under fast violent vibrations. The direct description allows to analyze, both intuitively and rigorously, the effect of vibrations in similar, and in more general, situations. The rigorous derivations in th...

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Bibliographic Details
Published in:Nonlinearity 2021-01, Vol.34 (1), p.394-410
Main Author: Artstein, Zvi
Format: Article
Language:English
Subjects:
stabilization
Stephenson-Kapitza pendulum
vibrational forces
violent vibrations
Young measures
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Summary:A simple intuitive physical explanation is offered, of the stability of the inverted pendulum under fast violent vibrations. The direct description allows to analyze, both intuitively and rigorously, the effect of vibrations in similar, and in more general, situations. The rigorous derivations in the paper follow a singular perturbations model of mixed slow and fast dynamics. The approach allows applications beyond the classical inverted pendulum model.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/abbe65