Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?статья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler’s paradox
(1952), has stimulated an ever 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. 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.