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Russia Moscow
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 Institute^{a} 
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 highfrequency 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 highfrequency periodic motions of a small amplitude which differ from the relative equilibria in the vertical is also studied for the system. 
Keywords  double pendulum, highfrequency oscillations, stability, KAMtheory 
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. 114129. 
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