O.V. Druzhinina1, E.V. Lisovsky2

1 FRC “Computer Science and Control” of RAS (Moscow)

1 V.A. Trapeznikov Institute of Control Sciences of RAS (Moscow)

2 Kaluga branch of the Bauman MSTU (Kaluga, Russia)

The analysis of stability-like properties for mathematical models of nonlinear dynamical systems and the description of qualitative effects based on the study of stability of various types are important scientific areas. The problems solving within the framework of these directions include the problems of finding conditions for stability and stabilization in the sense of N.E. Zhukovsky of trajectories of dynamic systems modeled by systems of three nonlinear differential equations of the first order. The purpose of the paper is to study the stability conditions in the Zhukovsky sense for the trajectories of dynamical systems described by three-dimensional systems of nonlinear differential equations using systems of equations of perturbed motion and special equations of the first approximation. The formulation of the stability problem in the Zhukovsky sense for the trajectories of dynamical systems described by systems of three nonlinear differential equations of the first order is considered. The concretization of the principle of reducing the Zhukovsky stability problem of the positive half-trajectory of the studied three-dimensional dynamic system to the Lyapunov stability problem of solving a system of three differential equations of perturbed motion is presented. Stability conditions are obtained using the proposed concretization of the reduction principle. The structure of the equations in variations used to study the Zhukovsky stability based on the stability conditions of the first approximation is studied. The results can be used in problems of mathematical modeling and qualitative research of trajectories of nonlinear dynamic systems, as well as for the study of various processes in systems of natural science and technology.

Druzhinina O.V., Lisovsky E.V. Stability analysis of trajectories for three-dimensional nonlinear dynamical systems. Nonlinear World. 2023. V. 21. № 2. P. 69-75. DOI: https://doi.org/10.18127/j20700970-202302-06 (In Russian)

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