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Russian Academy of Sciences
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IssuesArchive of Issues2013-2pp.167-171

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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 2 November 2010
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892813000804
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