Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey

Oleg Kirillov, Ferdinand Verhulst

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

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 languageEnglish
Title of host publicationProceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009
PublisherAmerican Society of Mechanical Engineers(ASME)
Pages655-670
Number of pages16
Volume10
EditionPART B
ISBN (Print)9780791843833
DOIs
Publication statusPublished - 11 Dec 2009
EventASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009 - Lake Buena Vista, FL, United States
Duration: 13 Nov 200919 Nov 2009

Conference

ConferenceASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009
CountryUnited States
CityLake Buena Vista, FL
Period13/11/0919/11/09

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