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

    2015, Vol. 11, No. 4, pp.  671–683

    Author(s): Kholostova O. V.

    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. А 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
    Citation: Kholostova O. V., The interaction of resonances of the third and fourth orders in a Hamiltonian two-degree-of-freedom system, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 4, pp.  671–683
    DOI:10.20537/nd1504004


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