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

Oleg N. Kirillov, Ferdinand Verhulst

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Abstract

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.
Original languageEnglish
Title of host publicationNovel Mathematics Inspired by Industrial Challenges
EditorsMichael Günther, Wil Schilders
Place of PublicationCham
PublisherSpringer
Pages201-243
Number of pages43
Volume38
ISBN (Electronic)9783030961732
ISBN (Print)9783030961725
Publication statusPublished - 1 Mar 2022

Publication series

NameThe European Consortium for Mathematics in Industry
PublisherSpringer
ISSN (Print)1612-3956
ISSN (Electronic)2198-3283

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