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We give a method which generates sufficient conditions for instability ofequilibria for circulatory and gyroscopic conservative systems. The method isbased on the Gramians of a set of vectors whose coordinates are powers of theroots of the characteristic polynomial for the studied systems. New instabilityresults are obtained for general circulatory and gyroscopic conservativesystems. We also apply this method for studying the instability of motion for acharged particle in a stationary electromagnetic field.

Instability conditions for circulatory and gyroscopic conservative systems