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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2009-6pp.642-647

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L.D. Akulenko and S.V. Nesterov, "The stability of the equilibrium of a pendulum of variable length," J. Appl. Math. Mech. 73 (6), 642-647 (2009)
Year 2009 Volume 73 Issue 6 Pages 642-647
Title The stability of the equilibrium of a pendulum of variable length
Author(s) L.D. Akulenko (Moscow, Russia,
S.V. Nesterov (Moscow, Russia)
Abstract The frequencies and modes of parametric oscillations of a pendulum of variable length for values of the modulation index from the smallest to the limit admissible values are investigated. The limits of the resonance zones of the first four oscillation modes are constructed and investigated by analytical and numerical methods, and the fundamental qualitative properties of the higher modes are established. Complete degeneracy of the modes with even numbers, i.e., coincidence of the frequencies of the odd and even eigenmodes for admissible values of the modulation parameter, is proved. The global pattern of the limits of the regions of stability of the lower position of equilibrium is constructed and it is shown that it differs considerably from the Ince-Strutt diagrams. Specific properties of the eigenmodes are established.
Received 29 December 2008
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