Abstract:
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.
Keywords:
natural mechanical system, degree of instability, gyroscopic and dissipative forces, retraction, Ważewski topological method, localized motions.
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Citation:
E. I. Kugushev, T. V. Salnikova, “Existence of Localized Motions in the Vicinity of an Unstable Equilibrium Position”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024, 128–139; Proc. Steklov Inst. Math., 327 (2024), 118–129
\Bibitem{KugSal24}
\by E.~I.~Kugushev, T.~V.~Salnikova
\paper Existence of Localized Motions in the Vicinity of an Unstable Equilibrium Position
\inbook Mathematical Aspects of Mechanics
\bookinfo Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 327
\pages 128--139
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4408}
\crossref{https://doi.org/10.4213/tm4408}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 327
\pages 118--129
\crossref{https://doi.org/10.1134/S0081543824060117}
Citation in format AMSBIB
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