Vasily Nikonov

    Leninskie gory 1, Moscow, 119991, Russia
    Lomonosov Moscow State University


    Burov A. A., Kosenko I., Nikonov V. I.
    The motion of a spacecraft containing a moving massive point in the central field of Newtonian attraction is considered. Within the framework of the so-called “satellite approximation”, the center of mass of the system is assumed to move in an unperturbed elliptical Keplerian orbit. The spacecraft’s dynamics about its center of mass is studied. Conditions under which the spacecraft rotates about a perpendicular to the plane of the orbit uniformly with respect to the true anomaly are found. Such uniform rotations are achieved using a specially selected rule for changing the position of a massive point with respect to the spacecraft. Necessary conditions for these uniform rotations are studied numerically. An analysis of the nonintegrability of a special class of spacecraft’s rotation is carried out using the method of separatrix splitting. Poincaré sections are constructed for certain parameter values. Several linearly stable periodic motions are pointed out and investigated.
    Keywords: spacecraft attitude dynamics, spacecraft in an elliptic orbit, spacecraft with variable mass distribution, spacecraft’s chaotic oscillations, spacecraft’s periodic motions
    Citation: Burov A. A., Kosenko I., Nikonov V. I.,  Spacecraft with Periodic Mass Redistribution: Regular and Chaotic Behaviour, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 4, pp.  639-649
    Burov A. A., Nikonov V. I.
    The problem of the existence and stability of relative equilibria (libration points) of a uniformly rotating gravitating body, which is a homogeneous ball with a spherical cavity, is considered. It is assumed that the rotation is carried out around an axis perpendicular to the axis of symmetry of the body and passing through its center of mass. The libration points located inside the cavity are investigated. Families of both isolated and nonisolated relative equilibria are found. Their stability and bifurcations are investigated. Realms of possible motion are constructed.
    Keywords: celestial bodies with cavities, libration points, relative equilibria, motion in a noncentral gravitational field, gravitating dumbbell
    Citation: Burov A. A., Nikonov V. I.,  Libration Points Inside a Spherical Cavity of a Uniformly Rotating Gravitating Ball, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 4, pp.  413-427
    Burov A. A., Nikonov V. I.
    As is well known, many small celestial bodies are of a rather complex shape. Therefore, the study of the dynamics of a spacecraft in their vicinity, based on terms up to the second order of smallness in the expansion of the potential of attraction, seems to be insufficient for an adequate description of the observed dynamical effects related, for example, to positioning of the libration points.
    In this paper, such effects are demonstrated for spacecraft dynamics in the vicinity of the asteroid (2063) Bacchus. The libration points are computed for various approximations of the gravitational potential. The results of this computation are compared with similar results obtained before for the so-called Sludsky – Werner – Scheeres potential. The dependence of the structure of the regions of possible motions on approximation of the gravitational potential is also studied.
    Keywords: (2063) Bacchus, gravitational potential expansion, libration points, region of possible motion, Hill’s region, zero-velocity locus
    Citation: Burov A. A., Nikonov V. I.,  Inertial Characteristics of Higher Orders and Dynamics in a Proximity of a Small Celestial Body, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 2, pp.  259-273
    Burov A. A., Guerman A., Raspopova E., Nikonov V. I.
    It is well known that several small celestial objects are of irregular shape. In particular, there exist asteroids of the so-called “dog-bone” shape. It turns out that approximation of these bodies by dumb-bells, as proposed by V.V. Beletsky, provides an effective tool for analytical investigation of dynamics in vicinities of such bodies. There remains the question of how to divide reasonably a “dogbone” body into two parts using available measurement data.
    In this paper we introduce an approach based on the so-called $K$-mean algorithm proposed by the prominent Polish mathematician H. Steinhaus.
    Keywords: $K$-means algorithm, small celestial bodies, mesh representation of an asteroid’s surface
    Citation: Burov A. A., Guerman A., Raspopova E., Nikonov V. I.,  On the use of the $K$-means algorithm for determination of mass distributions in dumbbell-like celestial bodies, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  45-52
    Burov A. A., Guerman A., Kosenko I., Nikonov V. I.
    The problem of the motion of a particle in the gravity field of a homogeneous dumbbell-like body composed of a pair of intersecting balls, whose radii are, in general, different, is studied. Approximation for the Newtonian potential of attraction is obtained. Relative equilibria and their properties are studied under the assumption of uniform rotation of the dumbbells.
    Keywords: generalized planar two-bodies problem, asteroid-like systems, gravitating systems with irregular mass distribution, stability of steady motions, bifurcations of steady motions
    Citation: Burov A. A., Guerman A., Kosenko I., Nikonov V. I.,  On the gravity of dumbbell-like bodies represented by a pair of intersecting balls, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 2, pp.  243-256
    Burov A. A., Nikonov V. I.
    The planar motion of an equilateral triangle with equal masses at vertices and of a point subjected to mutual Newtonian attraction is considered. Necessary conditions for the stability of “straight”, axial steady configurations, when the massive point is located on one of the symmetry axes of the triangle, are studied. The generation of other, “oblique”, steady configurations is discussed in connection with the variation, for certain parameter values, of the degree of instability of some “straight” steady configurations.
    Keywords: generalized planar two-body problem, asteroid-like systems, gravitating systems with irregular mass distribution, stability of steady motions, necessary conditions for stability, gyroscopic stabilization, bifurcations of steady motions, Poincaré bifurcation diagrams
    Citation: Burov A. A., Nikonov V. I.,  Stability and branching of stationary rotations in a planar problem of motion of mutually gravitating triangle and material point, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 2, pp.  179-196

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