|
ИСТИНА |
Войти в систему Регистрация |
ИПМех РАН |
||
On Periodic Poincare Motions in the Case of Degeneracy of an Unperturbed Systemстатья
Статья опубликована в журнале из списка RSCI Web of Science
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 15 апреля 2020 г.
- Автор: Markeev A.P.
- Журнал: Regular and Chaotic Dynamics
- Том: 25
- Номер: 1
- Год издания: 2020
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 111
- Последняя страница: 120
- DOI: 10.1134/S1560354720010098
- Аннотация: This paper is concerned with a one-degree-of-freedom system close to an integrable system. It is assumed that the Hamiltonian function of the system is analytic in all its arguments, its perturbing part is periodic in time, and the unperturbed Hamiltonian function is degenerate. The existence of periodic motions with a period divisible by the period of perturbation is shown by the Poincar´e methods. An algorithm is presented for constructing them in the form of series (fractional degrees of a small parameter), which is implemented using classical perturbation theory based on the theory of canonical transformations of Hamiltonian systems. The problem of the stability of periodic motions is solved using the Lyapunov methods and KAM theory. The results obtained are applied to the problem of subharmonic oscillations of a pendulum placed on a moving platform in a homogeneous gravitational field. The platform rotates with constant angular velocity about a vertical passing through the suspension point of the pendulum, and simultaneously executes harmonic small-amplitude oscillations along the vertical. Families of subharmonic oscillations of the pendulum are shown and the problem of their Lyapunov stability is solved.
- Добавил в систему: Маркеев Анатолий Павлович
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|