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This article is cited in 5 scientific papers (total in 5 papers)
Original papers
On the stability of stationary rotations in the approximate problem of motion of Lagrange’s top with a vibrating suspension point
M. V. Belichenko, O. V. Kholostova Moscow Aviation Institute (National Research University),
Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia
Abstract:
We consider the motion of Lagrange’s top with a suspension point performing the specified highfrequency periodic motion with small amplitude in three-dimensional space. The approximate autonomous system of equations of motion written in the form of canonical Hamiltonian equations is investigated. The problem of the existence and number of stationary rotations of the top about its dynamical symmetry axis is solved. The study of stability of the corresponding equilibrium positions of the reduced two-degree-of-freedom system for fixed values of the cyclic integral constant depending on the angular velocity of rotation is carried out. For suspension points’ motions allowing for stationary rotations about the vertical, a detailed linear and nonlinear stability analysis of these rotations and rotations about inclined axes is carried out. For a number of other cases of the suspension point motions a linear stability analysis is carried out.
Keywords:
Lagrange’s top, “sleeping” top, high-frequency vibrations, stability.
Received: 04.11.2016 Accepted: 10.12.2016
Citation:
M. V. Belichenko, O. V. Kholostova, “On the stability of stationary rotations in the approximate problem of motion of Lagrange’s top with a vibrating suspension point”, Nelin. Dinam., 13:1 (2017), 81–104
Linking options:
https://www.mathnet.ru/eng/nd552 https://www.mathnet.ru/eng/nd/v13/i1/p81
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Abstract page: | 312 | Full-text PDF : | 235 | References: | 39 |
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