 | | 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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| O.V. Kholostova, "Non-linear oscillations of a Hamiltonian system with two degrees of freedom with 2:1 resonance," J. Appl. Math. Mech. 74 (5), 563-578 (2010) |
| Year |
2010 |
Volume |
74 |
Issue |
5 |
Pages |
563-578 |
| Title |
Non-linear oscillations of a Hamiltonian system with two degrees of freedom with 2:1 resonance |
| Author(s) |
O.V. Kholostova (Moscow, Russia, kholostova_o@mail.ru) |
| Abstract |
The motions of an autonomous Hamiltonian system with two degrees of freedom close to an equilibrium position, stable in the linear approximation, are considered. It is assumed that in this neighbourhood the quadratic part of the Hamiltonian of the system is sign-variable, and the ratio of the frequencies of the linear oscillations are close to or equal to two. It is also assumed that the corresponding resonance terms in the third-degree terms of the Hamiltonian are small. The problem of the existence, bifurcations and orbital stability of the periodic motions of the system near the equilibrium position is solved. Conditionally periodic motions of the system are investigated. An estimate is obtained of the region in which the motions of the system are bounded in the neighbourhood of an unstable equilibrium in the case of exact resonance. The motions of a heavy dynamically symmetrical rigid body with a fixed point in the neighbourhood of its permanent rotations around the vertical for 2:1 resonance are considered as an application. |
| Received |
24 December 2009 |
| Link to Fulltext |
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