 | | 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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| Yu.N. Bibikov, "The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom," J. Appl. Math. Mech. 77 (2), 167-171 (2013) |
| Year |
2013 |
Volume |
77 |
Issue |
2 |
Pages |
167-171 |
| Title |
The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom |
| Author(s) |
Yu.N. Bibikov (St Petersburg, Russia, bibicoff@yandex.ru) |
| Abstract |
The stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom with a Hamiltonian, the unperturbed part of which generates oscillators with a cubic restoring force, is considered. It is proved that the equilibrium position is Lyapunov conditionally stable for initial values which do not belong to a certain surface of the Hamiltonian level. A reduction of the system onto this surface shows that, in the generic case, unconditional Lyapunov stability also occurs. |
| Received |
02 November 2010 |
| Link to Fulltext |
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