ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Stability of the State of Equilibrium of Some Essentially non-linear Hamiltonian Systems with Two Degrees of Freedom


Yu. N. Bibikov

Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department


A problem of the stability of the state of equilibrium of Hamiltonian systems with two degrees of freedom is considered. Systems under consideration describe motions of slightly coupled oscillators whose restoring forces are of odd degree. It is proved that if the restoring forces are not equal to each other, then the state of equilibrium is Liapunov stable. If they are equal to each other, then the case of the stability is generic.

Full text (pdf)