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В.А. Грибков, А.О. Хохлов

38

ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 2

possess the characteristics necessary for solving the two

experimental tasks (frequency testing tasks and the prob-

lems of defining the stability zone boundaries). We defined

stability zone experimental boundaries for a wide range of

change of amplitude and frequency excitation parameters.

By experiments we confirmed the theoretical prediction of

dynamical instability of inverted pendulum systems when

crossing the upper boundary of the stability zone. We

obtained the experimental results in the area connecting

the upper and lower boundary lines of the stability zone.

The results obtained in this work, were preceded by a

thorough analysis of the experimental material performed

by D.J. Acheson and T. Mullin for single, double and triple

pendulums

REFERENCES

[1] Akulenko L.D., Nesterov S.V. The stability of the equilibrium of a pendulum of variable

length.

Journal of Applied Mathematics and Mechanics

, 2009, vol. 73, no. 6, pp. 642–647.

DOI: 0.1016/j.jappmathmech.2010.01.004 Available at:

http://www.sciencedirect.com/

science/article/pii/S0021892810000055

[2] Arkhipova I.M., Luongo A., Seyranian A.P. Vibrational stabilization of the upright statically

unstable position of a double pendulum.

Journal of Sound and Vibration

, 2012, vol. 331, no. 2,

pp. 457–469. DOI: 10.1016/j.jsv.2011.09.007

Available at:

http://www.sciencedirect.com/science/article/pii/S0022460X11007425

[3] Aslanov B.C., Bezglasnyy S.P. Stability and instability of controlled motions of a two-mass

pendulum of variable length.

Mechanics of Solids

, 2012, vol. 47, no. 3, pp. 285–297.

DOI: 10.3103/S002565441203003X

Available at:

http://link.springer.com/article/10.3103%2FS002565441203003X

[4] Burov A.A., Kosenko I.I. Pendulum motions of extended lunar space elevator.

Mechanics

of Solids

, 2014, vol. 49, no. 5, pp. 506–517. DOI: 10.3103/S0025654414050033 Available at:

http://link.springer.com/article/10.3103/S0025654414050033

[5] Bulanchuk P.O., Petrov A.G. The vibrational energy and control of pendulum systems.

Journal of Applied Mathematics and Mechanics

, 2012, vol. 76, no. 4, pp. 396–404.

DOI: 10.1016/j.jappmathmech.2012.09.006 Available at:

http://www.sciencedirect.com/

science/article/pii/S0021892812000986

[6] Bulanchuk P.O., Petrov A.G. Suspension point vibration parameters for a given equilib-

rium of a double mathematical pendulum.

Mechanics of Solids

, 2013, vol. 48, no. 4, pp. 380–

387. DOI: 10.3103/S0025654413040043 Available at:

http://link.springer.com/article/10.3103/

S0025654413040043

[7] Zevin A.A., Filonenko L.A. Qualitative research on pendulum oscillations with cycling

length and mathematic model of seesaw.

Prikladnaya Matematika i Mekhanika

, 2007, vol. 71,

no. 6, pp. 989−1003 (in Russ.).

[8] Martynenko Yu.G., Formal'skiy A.M. Controlled pendulum on a movable base.

Mechanics

of Solids

, 2013, vol. 48, no. 1, pp. 6–18. DOI: 10.3103/S0025654413010020

Available at:

http://link.springer.com/article/10.3103/S0025654413010020