  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.
