On the instability of equilibria of conservative systems under typical degenerations
We study systems of differential equations admitting first integrals with degenerate critical points. We find conditions for the instability of equilibria for the cases in which the first integral loses the minimum property. Results of general nature are used in the proof of the impossibility of gyroscopic stabilization of equilibria in conservative mechanical systems under simple typical bifurcations.
KeywordsQuadratic Form Full System Conservative System Trivial Equilibrium Nontrivial Equilibrium
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