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On the One Method of Analyzing the Stability of Rest Points in Critical Cases
- Authors: Nesterov S.V.1
-
Affiliations:
- Ishlinsky Institute for Problems in Mechanics of the RAS
- Issue: Vol 87, No 4 (2023)
- Pages: 642-648
- Section: Articles
- URL: https://rjonco.com/0032-8235/article/view/675114
- DOI: https://doi.org/10.31857/S0032823523040094
- EDN: https://elibrary.ru/DZLVPR
- ID: 675114
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Abstract
For a two-dimensional oscillatory system with imaginary characteristic roots of linearized equations, a method is proposed that simplifies calculations and does not require the analyticity of the right-hand sides of the equations. The method is based on the decomposition of the vector function of the right-hand sides of the equations into solenoidal and potential components. Integral estimates for the stability of the equilibrium position are obtained.
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About the authors
S. V. Nesterov
Ishlinsky Institute for Problems in Mechanics of the RAS
Author for correspondence.
Email: bayd@ipmnet.ru
Russia, Moscow
References
- Poincaré H. Curves Defined by Differential Equations. Moscow; Leningrad: GITTL, 1947. (in Russian)
- Liapunov A.M. The General Problem of Stability of Motion. Moscow;Leningrad: GITTL, 1950. 471 p. (in Russian)
- Malkin I.G. Theory of Motion Stability. Moscow; Leningrad: GITTL, 1952. (in Russian)
- Lyapunov A.M. Investigation of One of the Special Cases of the Problem of Motion Stability. Leningrad: Leningrad Univ. Press, 1963.
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