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:
A. A. Burov, A. D. Guerman, E. A. Raspopova, V. I. Nikonov, “On the use of the K-means algorithm for determination of mass distributions in dumbbell-like celestial bodies”, Nelin. Dinam., 14:1 (2018), 45–52
\Bibitem{BurGueRas18}
\by A.~A.~Burov, A.~D.~Guerman, E.~A.~Raspopova, V.~I.~Nikonov
\paper On the use of the $K$-means algorithm for determination of mass distributions in dumbbell-like celestial bodies
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 1
\pages 45--52
\mathnet{http://mi.mathnet.ru/nd595}
\crossref{https://doi.org/10.20537/nd1801004}
\elib{https://elibrary.ru/item.asp?id=32773037}
Linking options:
https://www.mathnet.ru/eng/nd595
https://www.mathnet.ru/eng/nd/v14/i1/p45
This publication is cited in the following 6 articles:
E. A. Nikonova, “On the Maxwell Representation of the Gravitational Potential for a Symmetric Body”, Mech. Solids, 59:4 (2024), 1881
E. A. Nikonova, “Isosceles tetrahedron and an equimomental system of a rigid body”, Vestn. St. Petersbg. Univ., Math., 56:1 (2023), 119–124
V. I. Nikonov, “Multipole representation of the gravitational field for asteroid (16) Psyche”, Comput. Math. Math. Phys., 63:12 (2023), 2572–2579
A. A. Burov, A. D. Guerman, V. I. Nikonov, “Using the K-means method for aggregating the masses of elongated celestial bodies”, Cosmic Res., 57:4 (2019), 266–271
A. A. Burov, A. D. Guerman, E. A. Nikonova, V. I. Nikonov, “Approximation for attraction field of irregular celestial bodies using four massive points”, Acta Astronaut., 157 (2019), 225–232
A. A. Burov, A. D. German, V. I. Nikonov, “Gravitation fields approximation for some kinds of small celestial bodies on the base field of four attracting centers”, XLIII Academic Space Conference, Dedicated to the Memory of Academician S P Korolev and Other Outstanding Russian Scientists - Pioneers of Space Exploration, AIP Conf. Proc., 2171, eds. E. Mikrin, D. Rogozin, A. Aleksandrov, V. Sadovnichy, I. Fedorov, V. Mayorova, Amer. Inst. Phys., 2019, 060012
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