 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10482 |
| In Russian (ΟΜΜ): | | 9683
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| In English (J. Appl. Math. Mech.): | | 799 |
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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, kumak@ipmnet.ru)
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 |
| Link to Fulltext |
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