Existence of Localized Motions in the Vicinity of an Unstable Equilibrium Position

We consider a dynamical system whose equilibrium position is nondegenerate and Lyapunov unstable, the degree of instability being greater than zero and less than the number of degrees of freedom. We show that for any sufficiently small positive value of the total energy of the system, there exists a...

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Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 327; no. 1; pp. 118 - 129
Main Authors Kugushev, E. I., Salnikova, T. V.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2024
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Dynamical systems
Mathematics
Mathematics and Statistics
localized motions
retraction
Ważewski topological method
34D10
natural mechanical system
degree of instability
gyroscopic and dissipative forces
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Summary:We consider a dynamical system whose equilibrium position is nondegenerate and Lyapunov unstable, the degree of instability being greater than zero and less than the number of degrees of freedom. We show that for any sufficiently small positive value of the total energy of the system, there exists a motion of the system with this energy that starts at the boundary of the region of possible motion and does not leave a small neighborhood of the equilibrium position. Such motions are called localized motions.
Bibliography:ObjectType-Article-1
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SourceType-Conference Papers & Proceedings-1
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ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543824060117