 | | 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: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| L.A. Klimina, B.Ya. Lokshin, and V.A. Samsonov, "Bifurcation diagram of the self-sustained oscillation modes for a system with dynamic symmetry," J. Appl. Math. Mech. 81 (6), 442-449 (2017) |
| Year |
2017 |
Volume |
81 |
Issue |
6 |
Pages |
442-449 |
| DOI |
10.1016/j.jappmathmech.2018.03.012 |
| Title |
Bifurcation diagram of the self-sustained oscillation modes for a system with dynamic symmetry |
| Author(s) |
L.A. Klimina (Institute of Mechanics of the Lomonosov Moscow State University, Moscow, Russia)
B.Ya. Lokshin (Institute of Mechanics of the Lomonosov Moscow State University, Moscow, Russia)
V.A. Samsonov (Institute of Mechanics of the Lomonosov Moscow State University, Moscow, Russia, samson@imec.msu.ru) |
| Abstract |
An autonomous dynamical system with one degree of freedom is considered which possesses properties such that an asymptotically stable equilibrium becomes unstable after a certain parameter passes through zero and two new symmetrically arranged equilibria are created alongside it. It is known that, for sufficiently small values of the above mentioned parameter, bifurcation can be accompanied by the occurrence of periodic trajectories (cycles). To describe them, a bifurcation diagram of the relation between the amplitude of the cycles and the parameter, which characterizes the dissipation and takes finite values, is constructed. The results obtained are illustrated using the example of an investigation of the self-induced oscillatory modes in a model of an aerodynamic pendulum that takes account of the displacement of the pressure centre when the angle of attack is changed. |
| Keywords |
self-sustained oscillation |
| Received |
06 June 2017 |
| Link to Fulltext |
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