0
2013
Impact Factor

    On a Method of Introducing Local Coordinates in the Problem of the Orbital Stability of Planar Periodic Motions of a Rigid Body

    2020, Vol. 16, no. 4, pp.  581-594

    Author(s): Bardin B. S.

    A method is presented of constructing a nonlinear canonical change of variables which makes it possible to introduce local coordinates in a neighborhood of periodic motions of an autonomous Hamiltonian system with two degrees of freedom. The problem of the orbital stability of pendulum-like oscillations of a heavy rigid body with a fixed point in the Bobylev – Steklov case is discussed as an application. The nonlinear analysis of orbital stability is carried out including terms through degree six in the expansion of the Hamiltonian function in a neighborhood of the unperturbed periodic motion. This makes it possible to draw rigorous conclusions on orbital stability for the parameter values corresponding to degeneracy of terms of degree four in the normal form of the Hamiltonian function of equations of perturbed motion.
    Keywords: rigid body, rotations, oscillations, orbital stability, Hamiltonian system, local coordinates, normal form
    Citation: Bardin B. S., On a Method of Introducing Local Coordinates in the Problem of the Orbital Stability of Planar Periodic Motions of a Rigid Body, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 4, pp.  581-594
    DOI:10.20537/nd200404


    Download File
    PDF, 319.85 Kb




    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License