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RAS Energy, Mechanics & ControlПрикладная математика и механика Journal of Applied Mathematics and Mechanics

  • ISSN (Print) 0032-8235
  • ISSN (Online) 3034-5758

On the One Method of Analyzing the Stability of Rest Points in Critical Cases

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PII
10.31857/S0032823523040094-1
DOI
10.31857/S0032823523040094
Publication type
Status
Published
Authors
V. G. Baydulov
  • Affiliation: Ishlinsky Institute for Problems in Mechanics of the RAS
Volume/ Edition
Volume 87 / Issue number 4
Pages
642-648
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
устойчивость положения равновесия методы Ляпунова
Date of publication
01.04.2023
Year of publication
2023
Number of purchasers
0
Views
37

References

  1. 1. Пуанкаре А. О кривых, определяемых дифференциальными уравнениями, М.; Л.: ГИТТЛ, 1947.
  2. 2. Ляпунов А.М. Общая задача об устойчивости движения. М.; Л.: ГИТТЛ, 1950.
  3. 3. Малкин И.Г. Теория устойчивости движения. М.; Л.: ГИТТЛ, 1952.
  4. 4. Ляпунов А.М. Исследование одного из особенных случаев задачи об устойчивости движения. Л.: Изд-во Ленинградского университета, 1963.
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