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On dynamical stability of trajectories of nonlinear differential systems

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Druzhinina O.V.


The notion of stability in the sense of Joukovskij of dynamical system described by nonlinear autonomous multidimensional differential equation is considered in the paper. The comparative analysis of dynamical stability with stability in the sense of Lyapunov and orbital stability of trajectory is given. It was shown that geodetic of dynamical system on compact Riemannian space is exponentially dynamically under the condition of negativity of Ricci curvature. The main theorem is proved by the aid of method of moving coordinate frame and equation in variations of Joukovskij. It was shown that the notions of dynamical stability and dynamical instability of trajectories of differential systems play the important role for problems of chaotic dynamics of systems. The obtained results may be used for investigation of dynamics chaos in lateral dynamics of systems of railway transport, for investigation of turbulence in hydrodynamics and for study of other dynamical processes of natural science and technics.
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