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Acta Mechanica Sinica

, Volume 27, Issue 1, pp 2–6 | Cite as

Dissipation-induced instabilities and symmetry

  • Oleg N. Kirillov
  • Ferdinand Verhulst
Review

Abstract

The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler’s paradox (1952), has stimulated a 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, associated with Whitney’s umbrella. The first explanation of Ziegler’s paradox was given (much earlier) by Oene Bottema in 1956. The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.

Keywords

Dissipation-induced instabilities Destabilization paradox Ziegler pendulum Whitney umbrella 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH 2011

Authors and Affiliations

  1. 1.Dynamics and Vibrations Group, Department of Mechanical EngineeringTechnical University of Darmstadt Hochschulstr. 1DarmstadtGermany
  2. 2.Mathematisch InstituutUniversity of UtrechtUtrechtthe Netherlands

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