Classical Kapitsa’s problem of stability of an inverted pendulum and some generalizations

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Classical Kapitsa’s problem of stability of an inverted pendulum and some generalizations. / Belyaev, A. K.; Morozov, N. F.; Tovstik, P. E.; Tovstik, T. M.; Tovstik, T. M.

в: Acta Mechanica, Том 232, № 5, 05.2021, стр. 1743-1759.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{61f0e657d58b4a64bd042ec4b4c8c372,

title = "Classical Kapitsa{\textquoteright}s problem of stability of an inverted pendulum and some generalizations",

abstract = "The classical Kapitsa{\textquoteright}s problem of stability of an inverted pendulum subjected to vertical vibration of the support and some generalizations are investigated. The asymptotic method of two-scale expansions allows one to determine the level of vibrations that stabilizes the vertical position of the rod. The cases of inextensible and extensible rod are studied, and a benchmark of results is carried out. An attraction basin of the stable vertical position of the rod is found. Both harmonic and random stationary vibrations of the support are considered, too. Stability and attraction basin of the vertical position for a flexible rod are studied in detail. A single-mode approximation is used for the approximate solution to the nonlinear problem of stability of a flexible rod.",

author = "Belyaev, {A. K.} and Morozov, {N. F.} and Tovstik, {P. E.} and Tovstik, {T. M.} and Tovstik, {T. M.}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, AT part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = may,

doi = "10.1007/s00707-020-02907-0",

language = "English",

volume = "232",

pages = "1743--1759",

journal = "Acta Mechanica",

issn = "0001-5970",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Classical Kapitsa’s problem of stability of an inverted pendulum and some generalizations

AU - Belyaev, A. K.

AU - Morozov, N. F.

AU - Tovstik, P. E.

AU - Tovstik, T. M.

PY - 2021/5

Y1 - 2021/5

N2 - The classical Kapitsa’s problem of stability of an inverted pendulum subjected to vertical vibration of the support and some generalizations are investigated. The asymptotic method of two-scale expansions allows one to determine the level of vibrations that stabilizes the vertical position of the rod. The cases of inextensible and extensible rod are studied, and a benchmark of results is carried out. An attraction basin of the stable vertical position of the rod is found. Both harmonic and random stationary vibrations of the support are considered, too. Stability and attraction basin of the vertical position for a flexible rod are studied in detail. A single-mode approximation is used for the approximate solution to the nonlinear problem of stability of a flexible rod.

AB - The classical Kapitsa’s problem of stability of an inverted pendulum subjected to vertical vibration of the support and some generalizations are investigated. The asymptotic method of two-scale expansions allows one to determine the level of vibrations that stabilizes the vertical position of the rod. The cases of inextensible and extensible rod are studied, and a benchmark of results is carried out. An attraction basin of the stable vertical position of the rod is found. Both harmonic and random stationary vibrations of the support are considered, too. Stability and attraction basin of the vertical position for a flexible rod are studied in detail. A single-mode approximation is used for the approximate solution to the nonlinear problem of stability of a flexible rod.

UR - http://www.scopus.com/inward/record.url?scp=85101279325&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/75a77ab8-6661-3ec4-a738-eee0fc1eb90a/

U2 - 10.1007/s00707-020-02907-0

DO - 10.1007/s00707-020-02907-0

M3 - Article

AN - SCOPUS:85101279325

VL - 232

SP - 1743

EP - 1759

JO - Acta Mechanica

JF - Acta Mechanica

SN - 0001-5970

IS - 5

ER -

ID: 76383538