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# 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

Author(s): Burov A. A., Guerman A., Raspopova E., Nikonov V.

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