Dissipation-induced instabilities and symmetry |
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Authors: | Oleg N Kirillov Ferdinand Verhulst |
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Institution: | (2) Mathematisch Instituut, University of Utrecht, Utrecht, The Netherlands; |
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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. |
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Keywords: | Dissipation-induced instabilities · Destabilization paradox · Ziegler pendulum · Whitney umbrella |
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