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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

Nelin. Dinam., 2015 Volume 11, Number 4, Pages 671–683 (Mi nd501)

This article is cited in 5 papers

Original papers

The interaction of resonances of the third and fourth orders in a Hamiltonian two-degree-of-freedom system

O. V. Kholostova

Moscow Aviation Institute (National Research University), Volokolamskoe Shosse, 4, GSP-3, A-80, Moscow, 125993, Russia

Abstract: The motion of a time-periodic two-degree-of-freedom Hamiltonian system in the neighborhood of the equilibrium being stable in the linear approximation is considered. The weak Raman thirdorder resonance and the strong fourth-order resonance are assumed to occur simultaneously in the system. The behavior of the approximated (model) system is studied in the stability domain of the fourth-order resonance. Areas of the parameters (coefficients of the normalized Hamiltonian) are found for which all motions of the system are bounded if they begin in a sufficiently small neighborhood of the equilibrium. Boundedness domain estimate is obtained. À disturbing effect of the double resonance on the motion of the system within the boundedness domain is described.

Keywords: Hamiltonian system, canonical transformation, method of normal forms, double resonance, stability.

UDC: 531.36

MSC: 70H05, 70H14, 70H15, 70K45

Received: 18.08.2015
Revised: 08.10.2015



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