Attraction basins in the generalized Kapitsa’s problem

Cover Page

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

Russian Federation, 7/9, Universitetskaya embankment, Saint-Petersburg, 199034

Academician of the Russian Academy of Sciences

А. 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

  1. Stephenson A. // Phil. Mag. 1908. V. 15. P. 233-236.
  2. Капица П. Л. // Усп. физ. наук. 1951. Т. 44. № 1. С. 7-20.
  3. Блехман И. И. Вибрационная механика. М.: Наука, 1994.
  4. Блехман И. И. Теория вибрационных процессов и устройств. СПб.: ИД “Руда и металлы”, 2013.
  5. Морозов Н. Ф., Беляев А. К., Товстик П. Е., Товстик Т. П. // ДАН. 2018. Т. 482. № 2. С. 155-159.
  6. 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.
  7. Леонов Г. А., Шумафов М. М. Методы стабилизации линейных управляемых систем. СПб.: Изд-во СПб. ун-та, 2005.
  8. Боголюбов Н. Н., Митропольский Ю. А. Асимптотические методы в теории нелинейных колебаний. М.: Наука, 1969.
  9. Пугачев В. С. Теория случайных функций. М.: Физматлит, 1960.
  10. Гнеденко Б. В. Курс теории вероятностей. М.: Физматлит, 1961.

Statistics

Views

Abstract - 94

PDF (Russian) - 66

PlumX


Copyright (c) 2019 Russian academy of sciences

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies