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2013
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# Anna Guerman

Convento de Sto. António. 6201-001 Covilhã, Portugal
anna@ubi.pt
Centre for Aerospace Science and Technologies, University of Beira Interior

## Publications:

 Burov A. A., Guerman A., Raspopova E., Nikonov V. 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. Keywords: $K$-means algorithm, small celestial bodies, mesh representation of an asteroid’s surface Citation: Burov A. A., Guerman A., Raspopova E., Nikonov V.,  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 DOI:10.20537/nd1801004
 Burov A. A., Guerman A., Kosenko I., Nikonov V. 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. 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.,  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 DOI:10.20537/nd1702007