Authors' reply to 'A remark to the paper by O. N. Kirillov and F. Verhulst 'Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?'' [Zamm 90, No. 6, 462-488 (2010)].

The article discusses the aspect of the study regarding the paradoxes in the dissipation-induced destabilization or who opened Whitney's umbrella conducted by Oene Bottema. It mentions that the study with damping was compared with the domain of marginal stability and asymptotic stability depending on its characteristic polynomials. It states that he resolved it through the singularity theory on the boundary of two-degrees-of freedom non-conservative systems including the Ziegler's pendulum.