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On the stability degree. (English. Russian original) Zbl 1090.34564
Differ. Equ. 41, No. 2, 195-201 (2005); translation from Differ. Uravn. 41, No. 2, 186-192 (2005).
A Hamiltonian system of differential equations is considered. First, an inequality involving the indices of inertia of the corresponding quadratic form is presented. Then, this inequality is applied to infer results regarding the stability and the instability degrees of gyroscopic systems.

MSC:
34D05 Asymptotic properties of solutions to ordinary differential equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
34C60 Qualitative investigation and simulation of ordinary differential equation models
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