Motions of a two-degree-of-freedom Hamiltonian system in the presence of multiple third-order resonances

O. V. Kholostova

Russian journal of nonlinear dynamics, Tome 8 (2012) no. 2, pp. 267-288.

Résumé

Motions of a time-periodic, two-degree-of-freedom Hamiltonian system in a neighborhood of a linearly stable equilibrium are considered. It is assumed that there are several resonant thirdorder relations between the frequencies of linear oscillations of the system. It is shown that in the presence of two third-order resonances the equilibrium is unstable at any ratio between resonant coefficients. Approximate (model) Hamiltonians are obtained which are characteristic of the resonant cases under consideration. A detailed analysis is made of nonlinear oscillations of systems corresponding to them.

Détail

Keywords: Hamiltonian system, multiple resonance, stability
Mots-clés : Chetaev function.

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