Общая информация
Последний выпуск

Поиск публикаций
Поиск ссылок

Последний выпуск
Текущие выпуски
Архивные выпуски
Что такое RSS

Regul. Chaotic Dyn.:

Персональный вход:
Запомнить пароль
Забыли пароль?

Regul. Chaotic Dyn., 2019, том 24, выпуск 3, страницы 329–352 (Mi rcd481)  

A Parabolic Chaplygin Pendulum and a Paul Trap: Nonintegrability, Stability, and Boundedness

Alexey V. Borisovab, Alexander A. Kilinc, Ivan S. Mamaevde

a Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S.Kovalevskoi 16, Ekaterinburg, 620990 Russia
b A.A. Blagonravov Mechanical Engineering Research Institute of RAS, ul. Bardina 4, Moscow, 117334 Russia
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
d Center for Technologies in Robotics and Mechatronics Components, Innopolis University, ul. Universitetskaya 1, Innopolis, 420500 Russia
e Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia

Аннотация: This paper is a small review devoted to the dynamics of a point on a paraboloid. Specifically, it is concerned with the motion both under the action of a gravitational field and without it. It is assumed that the paraboloid can rotate about a vertical axis with constant angular velocity. The paper includes both well-known results and a number of new results.
We consider the two most widespread friction (resistance) models: dry (Coulomb) friction and viscous friction. It is shown that the addition of external damping (air drag) can lead to stability of equilibrium at the saddle point and hence to preservation of the region of bounded motion in a neighborhood of the saddle point. Analysis of three-dimensional Poincaré sections shows that limit cycles can arise in this case in the neighborhood of the saddle point.

Ключевые слова: parabolic pendulum, Paul trap, rotating paraboloid, internal damping, external damping, friction, resistance, linear stability, Hill’s region, bifurcational diagram, Poincaré section, bounded trajectory, chaos, integrability, nonintegrability, sepa

Финансовая поддержка Номер гранта
Российский научный фонд 15-12-00235
Министерство образования и науки Российской Федерации 5–100
The work of A.V.Borisov is supported by the program of the Presidium of the Russian Academy of Sciences no. 01 “Fundamental Mathematics and its Applications”. The work of A.A.Kilin (Section 3.2 and Appendix 1) is supported by the RSF grant no. 15-12-00235. The work of I. S.Mamaev is carried out at MIPT under project 5–100 for state support for leading universities of the Russian Federation.


Список литературы: PDF файл   HTML файл

Реферативные базы данных:

Тип публикации: Статья
MSC: 37J25, 37J05
Поступила в редакцию: 28.03.2019
Принята в печать:06.05.2019
Язык публикации: английский

Образец цитирования: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “A Parabolic Chaplygin Pendulum and a Paul Trap: Nonintegrability, Stability, and Boundedness”, Regul. Chaotic Dyn., 24:3 (2019), 329–352

Цитирование в формате AMSBIB
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper A Parabolic Chaplygin Pendulum and a Paul Trap: Nonintegrability, Stability, and Boundedness
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 3
\pages 329--352

Образцы ссылок на эту страницу:

    ОТПРАВИТЬ: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Просмотров:
    Эта страница:100
    Обратная связь:
     Пользовательское соглашение  Регистрация  Логотипы © Математический институт им. В. А. Стеклова РАН, 2020