A Parabolic Chaplygin Pendulum and a Paul Trap: Nonintegrability, Stability, and Boundedness

Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S.

doi:10.1134/s1560354719030067

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Destabilization By Friction1

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2022

2024

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Cited by 2 publications

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“…There are two cases that drastically change the stability (see also Bottema [26] and the recent works [23,135]) :…”

Section: Destabilization By Frictionmentioning

confidence: 99%

From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory

Kirillov

Verhulst

2022

Mathematics in Industry

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Four classical systems, the Kelvin gyrostat, the Maclaurin spheroids, the Brouwer rotating saddle, and the Ziegler pendulum have directly inspired development of the theory of Pontryagin and Krein spaces with indefinite metric and singularity theory as independent mathematical topics, not to mention stability theory and nonlinear dynamics. From industrial applications in shipbuilding, turbomachinery, and artillery to fundamental problems of astrophysics, such as asteroseismology and gravitational radiation -that is the range of phenomena involving the Krein collision of eigenvalues, dissipation-induced instabilities, and spectral and geometric singularities on the neutral stability surfaces, such as the famous Whitney's umbrella.

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“…There are two cases that drastically change the stability (see also Bottema [26] and the recent works [23,135]) :…”

Section: Destabilization By Frictionmentioning

confidence: 99%