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Gyroscopic stabilization and parametric resonance. (English. Russian original) Zbl 1038.70014
J. Appl. Math. Mech. 65, No. 5, 715-721 (2001); translation from Prikl. Mat. Mekh. 65, No. 5, 739-745 (2001).
The author studies small oscillations of a mechanical system near the equilibrium state which are described by the equations \(\ddot x + \Gamma\dot x +Px = 0\), \(x\in \mathbb R^n\), where \(\Gamma\) is a skew-symmetric \(n\times n\)-matrix, while the matrix \(P\) is symmetric. New sufficient conditions are established for gyroscopic stabilization of unstable equilibria by means of gyroscopic forces with a degenerate matrix.

MSC:
70J25 Stability for problems in linear vibration theory
70J40 Parametric resonances in linear vibration theory
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