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On the use of the $$K$$-means algorithm for determination of mass distributions in dumbbell-like celestial bodies. (Russian. English summary) Zbl 1395.70015
Summary: 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. Beletskiĭ, 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.
##### MSC:
 70F05 Two-body problems 70K20 Stability for nonlinear problems in mechanics 70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
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