Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?

Kirillov, Oleg and Verhulst, Ferdinand (2010) Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella? ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 90 (6). pp. 462-488. ISSN 0044-2267

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Official URL: http://dx.doi.org/10.1002/zamm.200900315

Abstract

The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an ever growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation, and related bifurcations.

Item Type: Article
Subjects: F300 Physics
G100 Mathematics
H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Oleg Kirillov
Date Deposited: 23 Jan 2017 12:29
Last Modified: 23 Jan 2017 12:50
URI: http://nrl.northumbria.ac.uk/id/eprint/29284

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