Abstract
The paradox of destabilization of a conservative or nonconservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an evergrowing 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.
Original language | English |
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Title of host publication | Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009 |
Publisher | American Society of Mechanical Engineers (ASME) |
Pages | 655-670 |
Number of pages | 16 |
Volume | 10 |
Edition | PART B |
ISBN (Print) | 9780791843833 |
DOIs | |
Publication status | Published - 11 Dec 2009 |
Event | ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009 - Lake Buena Vista, FL, United States Duration: 13 Nov 2009 → 19 Nov 2009 |
Conference
Conference | ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009 |
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Country/Territory | United States |
City | Lake Buena Vista, FL |
Period | 13/11/09 → 19/11/09 |