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Home » Issues » Archive of Issues » 2012 - 2 issue » pp. 114-129

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Russia Moscow
Year
2012
Issue
2
Pages
114-129
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Section Mechanics
Title To dynamics of a double pendulum with a horizontally vibrating point of suspension
Author(-s) Vishenkova E.A.a, Kholostova O.V.a
Affiliations Moscow Aviation Institutea
Abstract We consider the motion of a system consisting of two hinged thin uniform rods rotating about horizontal axes. It is assumed that the point of suspension of the system coinciding with the point of suspension of one of the rods makes horizontal high-frequency harmonic oscillations of a small amplitude. Investigation of stability of four relative equilibria in the vertical is carried out. It is proved that only the lower (''hanging") relative equilibrium can be stable if the oscillation frequency of the point of suspension doesn’t exceed the fixed value. For a system consisting of two identical rods the nonlinear problem of stability of this equilibrium is solved. The problem of existence, bifurcations and stability of high-frequency periodic motions of a small amplitude which differ from the relative equilibria in the vertical is also studied for the system.
Keywords double pendulum, high-frequency oscillations, stability, KAM-theory
UDC 531.36, 531.38
MSC 53A17, 70E20, 70E50
DOI 10.20537/vm120211
Received 30 September 2011
Language Russian
Citation Vishenkova E.A., Kholostova O.V. To dynamics of a double pendulum with a horizontally vibrating point of suspension, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 2, pp. 114-129.
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