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

    2012, Vol. 8, No. 2, pp.  267-288

    Author(s): Kholostova O. V.

    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.
    Keywords: Hamiltonian system, multiple resonance, stability, Chetaev function
    Citation: Kholostova O. V., Motions of a two-degree-of-freedom Hamiltonian system in the presence of multiple third-order resonances, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 2, pp.  267-288
    DOI:10.20537/nd1202005


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