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Estimating the Lyapunov function and stability of motion of a system with equations of motion with an asymptotically expanded right-hand side. (English. Russian original) Zbl 1462.34082

Int. Appl. Mech. 57, No. 1, 11-18 (2021); translation from Prikl. Mekh., Kiev 57, No. 1, 20-28 (2021).
Summary: New estimates of the Lyapunov function along the solutions of a system with an asymptotically expanded right-hand side are established. The deviation of the solutions of the averaged equations from the exact solutions of systems of equations under consideration is estimated. These estimates are used to establish new sufficient conditions for the stability of motion on a finite time interval and the estimation of an approximated solution of the systems of equations are established.

MSC:

34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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