Instability conditions for circulatory and gyroscopic conservative systems

Details Instability conditions for circulatory and gyroscopic conservative systems Instability conditions for circulatory and gyroscopic conservative systems

2011-12-06

arxiv.org/abs/1112.1192v2

Mathematics

Dynamical Systems

Scientific paper

We give a method which generates sufficient conditions for instability of equilibria for circulatory and gyroscopic conservative systems. The method is based on the Gramians of a set of vectors whose coordinates are powers of the roots of the characteristic polynomial for the studied systems. New instability results are obtained for general circulatory and gyroscopic conservative systems. We also apply this method for studying the instability of motion for a charged particle in a stationary electromagnetic field.

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