Dissipation-induced instabilities and symmetry

Kirillov, Oleg and Verhulst, Ferdinand (2011) Dissipation-induced instabilities and symmetry. Acta Mechanica Sinica, 27 (1). pp. 2-6. ISSN 0567-7718

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Official URL: http://dx.doi.org/10.1007/s10409-011-0409-0

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.

Item Type: Article
Additional Information: Published online 15th March 2011.
Uncontrolled Keywords: Dissipation-induced instabilities, destabilization paradox, Ziegler pendulum, Whitney umbrella
Subjects: F300 Physics
G100 Mathematics
H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Oleg Kirillov
Date Deposited: 23 Jan 2017 12:52
Last Modified: 31 Jan 2017 11:58
URI: http://nrl.northumbria.ac.uk/id/eprint/29280

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