Abstract A monodromy matrix calculated at a single arbitrary point of the periodic solution to a Hamiltonian system allows one to obtain both the direction of continuation for the family of solutions of the first (in Poincaré’s sense) kind and the multiplicity and direction of branching for periodic solutions of the second kind. In case of resonances 1 : 1 and 1 : 2 one needs to take into account the structure of elementary divisors of the monodromy matrix. Using the planar circular restricted three-body problem as an example, the infiniteness of the process of branching for a nonintegrable system and its finiteness for an integrable system are demonstrated. It is proved that periodic solutions of both first and second kinds which are obtained by continuation of symmetric periodic solutions of a restricted problem are also symmetric. The only exception is the case of resonance 1 : 1 and two second-order cells of the monodromy matrix in the Jordanian form. In this case, all periodic solutions of the second kind turned out to be nonsymmetrical. Examples of the families of nonsymmetrical periodic solutions are given.


    Access

    Access via TIB

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Families of periodic solutions to Hamiltonian systems: Nonsymmetrical periodic solutions for a planar restricted three-body problem


    Contributors:

    Published in:

    Publication date :

    2005




    Type of media :

    Article (Journal)


    Type of material :

    Print


    Language :

    English



    Classification :

    BKL:    55.60 Raumfahrttechnik / 39.00 Astronomie: Allgemeines / 50.93 Weltraumforschung
    Local classification TIB:    770/3520/8000