Every physical system is described by parameters, and one goal of the present contribution is to study the movements of eigenvalues in the complex plane depending on the system inherent parameters. A main focus lies in tracing the boundary curve which separates unstable from marginally stable domains in the parameter space. Hence, there is no need to study the whole parameter space but a certain subset which can be characterized by a zero eigenvalue. The method is illustrated by means of a static stability problem arising in the study of rotating blades.

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