Impact Factor

    Evgeniia Chekina


    Bardin B. S., Chekina E. A.
    The orbital stability of pendulum-like oscillations of a heavy rigid body with a fixed point in the Bobylev – Steklov case is investigated. In particular, a nonlinear study of the orbital stability is performed for the so-called case of degeneracy, where it is necessary to take into account terms of order six in the Hamiltonian expansion in a neighborhood of the unperturbed periodic orbit.
    Keywords: rigid body, rotations, oscillations, orbital stability, Hamiltonian system, local coordinates, normal form
    Citation: Bardin B. S., Chekina E. A.,  On the Orbital Stability of Pendulum-like Oscillations of a Heavy Rigid Body with a Fixed Point in the Bobylev – Steklov Case, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 4, pp.  453-464
    Bardin B. S., Chekina E. A.
    The motion of a rigid body satellite about its center of mass is considered. The problem of the orbital stability of planar pendulum-like rotations of the satellite is investigated. It is assumed that the satellite moves in a circular orbit and its geometry of mass corresponds to a plate. In unperturbed motion the minor axis of the inertia ellipsoid lies in the orbital plane.
    A nonlinear analysis of the orbital stability for previously unexplored values of parameters corresponding to the boundaries of the stability regions is carried out. The study is based on the normal form technique. In the special case of fast rotations a normalization procedure is performed analytically. In the general case the coefficients of normal form are calculated numerically. It is shown that in the case under consideration the planar rotations of the satellite are mainly unstable, and only on one of the boundary curves there is a segment where the formal orbital stability takes place.
    Keywords: satellite, rotations, orbital stability, Hamiltonian system, symplectic map, normal form, combinational resonance, resonance of essential type
    Citation: Bardin B. S., Chekina E. A.,  On Orbital Stability of Pendulum-like Satellite Rotations at the Boundaries of Stability Regions, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp.  415-428
    Bardin B. S., Chekina E. A.
    We deal with the problem of stability for a resonant rotation of a satellite. It is supposed that the satellite is a rigid body whose center of mass moves in an elliptic orbit. The resonant rotation is a planar motion such that the body completes one rotation in absolute space during two orbital revolutions of its center of mass. The stability analysis of the resonant rotation with respect to planar perturbations has been performed in detail earlier. In this paper we investigate the stability of the resonant rotation with respect to both planar and spatial perturbations for a nonsymmetric satellite. For small values of the eccentricity we have obtained boundaries of instability domains (parametric resonance domains) in an analytic form. For arbitrary eccentricity values we numerically construct domains of stability in linear approximation. Outside the above stability domains the resonant rotation is unstable in the sense of Lyapunov.
    Keywords: Hamiltonian system, resonant periodic motion, parametric resonance, satellite, stability
    Citation: Bardin B. S., Chekina E. A.,  On the stability of a resonant rotation of a satellite in an elliptic orbit, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  619–632

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