Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2012-4pp.388-392

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A.P. Markeyev, "The rotations of a pendulum excited by a high-frequency harmonic variation of its length," J. Appl. Math. Mech. 76 (4), 388-392 (2012)
Year 2012 Volume 76 Issue 4 Pages 388-392
Title The rotations of a pendulum excited by a high-frequency harmonic variation of its length
Author(s) A.P. Markeyev (Moscow, Russia, markeev@ipmnet.ru)
Abstract The motion of a mathematical pendulum, whose length is varied harmonically with time at a frequency that is high compared with the characteristic frequency of small oscillations of a pendulum of constant length, is considered. The method of canonical transformations and results obtained previously on Poincaré periodic motions in close to integrable Hamiltonian systems with one degree of freedom,1 are the basis of the investigation. It is shown that periodic motions of the pendulum exist that are close to its rotation with an angular frequency, the mean value of which over time is a multiple of the frequency with which the pendulum length changes. An explicit expression for the periodic motions is obtained in the first approximation with respect to the small parameter. The non-linear problem of the stability of Lyapunov periodic motions is solved.
Received 11 May 2011
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