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

Kirillov, Oleg and Verhulst, Ferdinand (2022) From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theory. In: Novel Mathematics Inspired by Industrial Challenges. The European Consortium for Mathematics in Industry, 38 . Springer, Cham, pp. 201-243. ISBN 9783030961725, 9783030961732

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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.

Item Type: Book Section
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Ay Okpokam
Date Deposited: 03 Dec 2019 14:59
Last Modified: 25 Jan 2022 14:30
URI: http://nrl.northumbria.ac.uk/id/eprint/41660

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