Regular and Chaotic Dynamics
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Regular and Chaotic Dynamics, 2017, том 22, выпуск 7, страницы 808–823
DOI: https://doi.org/10.1134/S1560354717070048
(Mi rcd292)
 

Эта публикация цитируется в 8 научных статьях (всего в 8 статьях)

On the Constructive Algorithm for Stability Analysis of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in the Second-order Resonance Case

Boris S. Bardinab, Evgeniya A. Chekinaa

a Department of Mechatronics and Theoretical Mechanics, Faculty of Information Technologies and Applied Mathematics, Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia
b Computer Modelling Laboratory, Department of Mechanics and Control of Machines, Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), M. Kharitonyevskiy per. 4, Moscow, 101990 Russia
Список литературы:
Аннотация: This paper is concerned with a nonautonomous Hamiltonian system with two degrees of freedom whose Hamiltonian is a $2\pi$-periodic function of time and analytic in a neighborhood of an equilibrium point. It is assumed that the system exhibits a secondorder resonance, i. e., the system linearized in a neighborhood of the equilibrium point has a double multiplier equal to $-1$. The case of general position is considered when the monodromy matrix is not reduced to diagonal form and the equilibrium point is linearly unstable. In this case, a nonlinear analysis is required to draw conclusions on the stability (or instability) of the equilibrium point in the complete system.
In this paper, a constructive algorithm for a rigorous stability analysis of the equilibrium point of the above-mentioned system is presented. This algorithm has been developed on the basis of a method proposed in [1]. The main idea of this method is to construct and normalize a symplectic map generated by the phase flow of a Hamiltonian system.
It is shown that the normal form of the Hamiltonian function and the generating function of the corresponding symplectic map contain no third-degree terms. Explicit formulae are obtained which allow one to calculate the coefficients of the normal form of the Hamiltonian in terms of the coefficients of the generating function of a symplectic map.
The developed algorithm is applied to solve the problem of stability of resonant rotations of a symmetric satellite.
Ключевые слова: Hamiltonian system, stability, symplectic map, normal form, resonant rotation, satellite.
Финансовая поддержка Номер гранта
Министерство образования и науки Российской Федерации 3.3858.2017/4.6
This work was carried out in Moscow Aviation Institute (National Research University) within the framework of the state assignment (project № 3.3858.2017/4.6).
Поступила в редакцию: 03.08.2017
Принята в печать: 19.10.2017
Реферативные базы данных:
Тип публикации: Статья
Язык публикации: английский
Образец цитирования: Boris S. Bardin, Evgeniya A. Chekina, “On the Constructive Algorithm for Stability Analysis of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in the Second-order Resonance Case”, Regul. Chaotic Dyn., 22:7 (2017), 808–823
Цитирование в формате AMSBIB
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\by Boris S. Bardin, Evgeniya A. Chekina
\paper On the Constructive Algorithm for Stability Analysis of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in the Second-order Resonance Case
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 7
\pages 808--823
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\crossref{https://doi.org/10.1134/S1560354717070048}
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  • https://www.mathnet.ru/rus/rcd292
  • https://www.mathnet.ru/rus/rcd/v22/i7/p808
  • Эта публикация цитируется в следующих 8 статьяx:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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