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

Oleg Kirillov, Ferdinand Verhulst

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Abstract

Three classical systems, the Kelvin gyrostat, the Maclaurin spheroids, 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.
Original languageEnglish
Title of host publicationNew mathematics inspired by industrial challenges
EditorsWil Schilders, Michael Guenther
PublisherSpringer
Number of pages40
Publication statusAccepted/In press - 1 Dec 2019

Publication series

NameThe European Consortium for Mathematics in Industry

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