Vasily Nikonov
Publications:
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Burov A. A., Nikonov V. I.
Inertial Characteristics of Higher Orders and Dynamics in a Proximity of a Small Celestial Body
2020, Vol. 16, no. 2, pp. 259-273
Abstract
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.
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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
2018, Vol. 14, no. 1, pp. 45-52
Abstract
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.
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Burov A. A., Guerman A., Kosenko I., Nikonov V. I.
On the gravity of dumbbell-like bodies represented by a pair of intersecting balls
2017, Vol. 13, No. 2, pp. 243-256
Abstract
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.
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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
2016, Vol. 12, No. 2, pp. 179-196
Abstract
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.
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