The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom

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 condi...

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Bibliographic Details
Published in:Journal of applied mathematics and mechanics 2013, Vol.77 (2), p.167-171
Main Author: Bibikov, Yu. N.
Format: Article
Language:English
Subjects:
Degrees of freedom
Mathematical analysis
Origins
Oscillators
Reduction
Renovating
Stability
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Summary: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.
ISSN:0021-8928
0021-8928
DOI:10.1016/j.jappmathmech.2013.07.006