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On the mechanism of stability loss. (English. Russian original) Zbl 1375.70018
Differ. Equ. 45, No. 4, 510-519 (2009); translation from Differ. Uravn. 45, No. 4, 496-505 (2009).
Summary: We consider linear systems of differential equations admitting functions in the form of quadratic forms that do not increase along trajectories in the course of time. We find new relations between the inertia indices of these forms and the instability degrees of the equilibria. These assertions generalize well-known results in the oscillation theory of linear systems with dissipation and clarify the mechanism of stability loss, whereby nonincreasing quadratic forms lose the property of minimum.

MSC:
70E50 Stability problems in rigid body dynamics
70E05 Motion of the gyroscope
34D20 Stability of solutions to ordinary differential equations
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