Email this article 
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://journals.rcsi.science/0032-8235/article/view/138884
- DOI: https://doi.org/10.31857/S0032823523040094
- EDN: https://elibrary.ru/DZLVPR
- ID: 138884
Cite item
Full Text
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.
Keywords
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.
Supplementary files
