16.
Андронов А.А.
,
Леонтович М.А.
О колебаниях системы с периодически меняю-
щимися параметрами // Журн. русск. физ.-хим. общ. Часть физич. 1927. Т. 59.
Вып. 5–6. C. 429–443.
17.
Бардин Б.С.
,
Маркеев А.П.
Об устойчивости равновесия маятника при верти-
кальных колебаниях точки подвеса // Прикладная математика и механика. 1995.
Т. 59. Вып. 6. С. 923–929.
18.
Челомей С.В.
О двух задачах динамической устойчивости колебательных си-
стем, поставленных академиками П.Л. Капицей и В.Н. Челомеем // Изв. АН
СССР. МТТ. 1999. № 6. С. 159–166.
19.
Otterbein S.
Stabilisierung des
n
-Pendels und der Indische Seiltrick // Archive for
Rational Mechanics and Analysis, 1982. Vol. 78. Р. 381–393.
20.
Floquet G.
Sur les ´equations diff´erentielles lin´eaires `a coefficients p´eriodiques // Ann.
Sci. ´Ecole Norm. Sup. 1883. Vol. 12. Р. 47–89.
21.
Четаев Н.Г.
Устойчивость движения. М.: Наука, 1990. 176 с.
REFERENCES
[1] Сhelomey V.N. Paradoxes in mechanics, vibrations caused.
Doklady Akademii Nauk
SSSR
[Proc. of the USSR Akademy of Sciences], 1983. vol. 270, no. 1. pp. 62–67
(in Russ.).
[2] Stephenson A. On a New Type of Dynamical Stability.
Memoirs and Proceedings
of the Manchester Literary and Philosophical Society
, 1908, vol. 52, no. 8, part II,
pp. 1–10.
[3] Bogolyubov N.N. Perturbation Theory in Nonlinear Mechanics.
Sb. Inst. Stroitelnoy
mehaniki AN USSR
[Collection of Papers of the Institute of Structural Mechanics
Academy of Science of Ukraine], 1950, vol. 14, no. 2. pp. 9–34 (in Russ.).
[4] Kapitsa P.L. Dynamic Stability of a Pendulum with a Vibrating Suspension Point.
Zh. Eksp. Teor. Fiz.
[J. Exp. Theor. Phys.], 1951, vol. 21, no. 5, pp. 588–597 (in
Russ.).
[5] Kapitsa P.L. The Pendulum with a Vibrating Suspension.
Usp. Fiz. Nauk
[Sov. Phys.-
Usp.], 1951, vol. 44, no. 1. pp. 7–20 (in Russ.).
[6]
Arkhipova I.M., Luongo A. Seyranian A.P.
Vibrational Stabilization of the Upright
Statically Unstable Position of a Double Pendulum.
J. of Sound and Vibration
, 2012,
vol. 331. pp. 457–469.
[7] Sorokin V.S. Analysis of Motion of Inverted Pendulum with Vibrating Suspension
Axis at Low-Frequency Excitation as an Illustration of a New Approach for Solving
Equation without Explicit Small Parameter.
International J. of Non-Linear Mechanic
,
2014, vol. 63. July, pp. 1–9.
[8] Markeev A.P. On the Stability of Nonlinear Oscillations Coupled Pendulums.
Izv.
Akad. Nauk, Mekh. Tverd. Tela
[Mech. Solids], 2013, no. 4, pp. 20–30 (in Russ.).
[9] Beletskiy V.V., Levin E.M. Dinamika kosmicheskikh trosovykh system [The
Dynamics of Space Tether Systems]. Moscow, Nauka Publ., 1990. 336 p.
[10] Alpatov A.P., Beletskiy V.V., Dranovskiy V.I., Zakrzhevskiy A.E., Pirozhenko
A.V., Troger G., Horochilov V.S. Dinamika kosmicheskikh sistem s trosovymi i
sharnirnymi soedineniyami [Dynamics Space Systems and Rope Swivels]. Moscow–
Izhevsk, NIC Regul. i khaot. dinamika. Inst. Komp’yut. issl. Publ., 2007. 559 p.
[11] Strizhak T.G. Metod usredneniya v zadachakh mehaniki [The Averaging Method in
Mechanics Problems]. Kiev–Donetsk., Vysh. Shkola, 1982. 250 p.
[12] Acheson D.J., Mullin T. Upside-Down Pendulums.
Nature
, 1993, vol. 366, pp. 215–
216.
[13] Mathieu E. M´emoiresur le mouvement vibratoired´une membrane de formeelliptique.
Jour. de Math. Pureset Appliqu´es
(Jour. De Liouville), 1868, vol. 13, pp. 137–203.
48 ISSN 0236-3941. Вестник МГТУ им. Н.Э. Баумана. Сер. “Машиностроение”. 2015. № 6