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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

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International Applied Mechanics Aims and scope

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.

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova Str., Kyiv, 03057, Ukraine

    A.A. Martynyuk & V. A. Chernienko

Authors
  1. A.A. Martynyuk
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  2. V. A. Chernienko
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Correspondence to A.A. Martynyuk.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 57, No. 1, pp. 20–28, January–February 2021.

This study was sponsored by the budgetary program Support of Priority Areas of Research (KPKVK 6541230).

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Martynyuk, A., Chernienko, V.A. Estimating the Lyapunov Function and Stability of Motion of a System with Equations of Motion with an Asymptotically Expanded Right-Hand Side. Int Appl Mech 57, 11–18 (2021). https://doi.org/10.1007/s10778-021-01064-8

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  • DOI: https://doi.org/10.1007/s10778-021-01064-8

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