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Russia Dolgoprudnyi; Moscow
Year
2017
Volume
27
Issue
4
Pages
590-607
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Section Mechanics
Title A study of permanent rotations of a heavy dynamically symmetric rigid body with a vibrating suspension point
Author(-s) Vishenkova E.A.ab, Kholostova O.V.bc
Affiliations Research and Production Company “Infosystem-35”a, Moscow Aviation Instituteb, Moscow Institute of Physics and Technologyc
Abstract The motion of a dynamically symmetric rigid body in a uniform gravity field is considered for the case of vertical high-frequency harmonic oscillations of small amplitude of one of its points (the suspension point). The investigation is carried out within the framework of an approximate autonomous system of differential equations of motion written in the canonical Hamiltonian form. A detailed description of admissible arcs of permanent rotations of the body about vertical axes is given. Special cases of motions of the body are found which are caused by fast vibrations of the suspension point. One of these cases is studied when the rotation axis lies in the principal plane of inertia which does not contain the center of mass of the body and does not coincide with the equatorial plane of inertia. A complete nonlinear stability analysis of the corresponding equilibrium position of the two-degree-of-freedom system is carried out. For all admissible values of the three-dimensional parameter space, regions of linear stability are found. Cases of resonances of the third and fourth orders, as well as degeneration cases, are considered.
Keywords Staude's permanent rotations, high-frequency oscillations, rigid body, dynamic symmetry, stability, resonance
UDC 531.36, 531.38
MSC 53A17, 70E20, 70E50
DOI 10.20537/vm170409
Received 28 September 2017
Language Russian
Citation Vishenkova E.A., Kholostova O.V. A study of permanent rotations of a heavy dynamically symmetric rigid body with a vibrating suspension point, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 4, pp. 590-607.
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