Email this article 
Attraction basins in the generalized Kapitsa’s problem
- Authors: Morozov N.F.1, Belyaev А.К.2, Tovstik P.E.1, Tovstik T.M.1, Tovstik T.P.2
-
Affiliations:
- Saint-Petersburg State University
- Institute of Problems in Mechanical Engineering of Russian Academy of Sciences
- Issue: Vol 487, No 5 (2019)
- Pages: 502-506
- Section: Mechanics
- URL: https://journals.eco-vector.com/0869-5652/article/view/15889
- DOI: https://doi.org/10.31857/S0869-56524875502-506
- ID: 15889
Cite item
Open Access
Access granted
Subscription Access
Abstract
Stability of vertical position of an inverted pendulum under action of support vibration as well as the attraction basin of this position is considered. In addition to the classic Kapitsa problem for the harmonic vibration of support, the poly-harmonic and random vibration of support is investigated. The condition of stability of vertical position is determined and the attraction basin of this stable position is studied.
About the authors
N. F. Morozov
Saint-Petersburg State University
Author for correspondence.
Email: morozov@nm1016.spb.edu
Academician of the Russian Academy of Sciences
Russian Federation, 7/9, Universitetskaya embankment, Saint-Petersburg, 199034А. К. Belyaev
Institute of Problems in Mechanical Engineering of Russian Academy of Sciences
Email: morozov@nm1016.spb.edu
Russian Federation, 61, Bol'shoy prospect, V.O., St. Petersburg, 199178
P. E. Tovstik
Saint-Petersburg State University
Email: morozov@nm1016.spb.edu
Russian Federation, 7/9, Universitetskaya embankment, Saint-Petersburg, 199034
T. M. Tovstik
Saint-Petersburg State University
Email: morozov@nm1016.spb.edu
Russian Federation, 7/9, Universitetskaya embankment, Saint-Petersburg, 199034
T. P. Tovstik
Institute of Problems in Mechanical Engineering of Russian Academy of Sciences
Email: tovstik_t@mail.ru
Russian Federation, 61, Bol'shoy prospect, V.O., St. Petersburg, 199178
References
- Stephenson A. // Phil. Mag. 1908. V. 15. P. 233-236.
- Капица П. Л. // Усп. физ. наук. 1951. Т. 44. № 1. С. 7-20.
- Блехман И. И. Вибрационная механика. М.: Наука, 1994.
- Блехман И. И. Теория вибрационных процессов и устройств. СПб.: ИД “Руда и металлы”, 2013.
- Морозов Н. Ф., Беляев А. К., Товстик П. Е., Товстик Т. П. // ДАН. 2018. Т. 482. № 2. С. 155-159.
- Belyaev A. K., Morozov N. F., Tovstik P. E., Tovstik T. P. // Vestnik SPb Univ. Mathematics. Mechanics. Astronomy. M.: Pleades Publ., Ltd., 2018. V. 51 (3). P. 296-304.
- Леонов Г. А., Шумафов М. М. Методы стабилизации линейных управляемых систем. СПб.: Изд-во СПб. ун-та, 2005.
- Боголюбов Н. Н., Митропольский Ю. А. Асимптотические методы в теории нелинейных колебаний. М.: Наука, 1969.
- Пугачев В. С. Теория случайных функций. М.: Физматлит, 1960.
- Гнеденко Б. В. Курс теории вероятностей. М.: Физматлит, 1961.
Supplementary files
