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Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants. / Milanov, D. V.; Milanova, Yu V.; Kholshevnikov, K. V.

в: Celestial Mechanics and Dynamical Astronomy, Том 131, № 1, 5, 01.01.2019.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Milanov, DV, Milanova, YV & Kholshevnikov, KV 2019, 'Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants', Celestial Mechanics and Dynamical Astronomy, Том. 131, № 1, 5. https://doi.org/10.1007/s10569-019-9884-6

APA

Milanov, D. V., Milanova, Y. V., & Kholshevnikov, K. V. (2019). Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants. Celestial Mechanics and Dynamical Astronomy, 131(1), [5]. https://doi.org/10.1007/s10569-019-9884-6

Vancouver

Milanov DV, Milanova YV, Kholshevnikov KV. Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants. Celestial Mechanics and Dynamical Astronomy. 2019 Янв. 1;131(1). 5. https://doi.org/10.1007/s10569-019-9884-6

Author

Milanov, D. V. ; Milanova, Yu V. ; Kholshevnikov, K. V. / Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants. в: Celestial Mechanics and Dynamical Astronomy. 2019 ; Том 131, № 1.

BibTeX

@article{430e53297695459ab7e90493331401ab,
title = "Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants",
abstract = "In this article, we prove the relaxed triangle inequality for Southworth and Hawkins, Drummond and Jopek orbital similarity criteria on the set of non-rectilinear Keplerian orbits with the eccentricity bounded above. We give estimates of the minimal coefficients in the inequality for each criterion and show that one of the calculated coefficients is exactly minimal. The obtained inequalities can be used for the acceleration of algorithms involving pairwise distances calculations between orbits. We present an algorithm for calculation of all distances not exceeding a fixed number in a quasi-metric space and demonstrate that the algorithm is faster than the complete calculation on the set of meteors orbits. Finally, we estimate the correlation dimensions of the set of main belt asteroids orbits and meteors orbits with respect to various orbital metrics and quasi-metrics.",
keywords = "Clustering algorithm, Correlation dimension, Correlation integral, Distance matrix, Orbital similarity criterion, Quasi-metric, Relaxed triangle inequality, Space of Keplerian orbits, METEOR, SEARCH, EFFICIENT ALGORITHM",
author = "Milanov, {D. V.} and Milanova, {Yu V.} and Kholshevnikov, {K. V.}",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/s10569-019-9884-6",
language = "English",
volume = "131",
journal = "Celestial Mechanics and Dynamical Astronomy",
issn = "0923-2958",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants

AU - Milanov, D. V.

AU - Milanova, Yu V.

AU - Kholshevnikov, K. V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this article, we prove the relaxed triangle inequality for Southworth and Hawkins, Drummond and Jopek orbital similarity criteria on the set of non-rectilinear Keplerian orbits with the eccentricity bounded above. We give estimates of the minimal coefficients in the inequality for each criterion and show that one of the calculated coefficients is exactly minimal. The obtained inequalities can be used for the acceleration of algorithms involving pairwise distances calculations between orbits. We present an algorithm for calculation of all distances not exceeding a fixed number in a quasi-metric space and demonstrate that the algorithm is faster than the complete calculation on the set of meteors orbits. Finally, we estimate the correlation dimensions of the set of main belt asteroids orbits and meteors orbits with respect to various orbital metrics and quasi-metrics.

AB - In this article, we prove the relaxed triangle inequality for Southworth and Hawkins, Drummond and Jopek orbital similarity criteria on the set of non-rectilinear Keplerian orbits with the eccentricity bounded above. We give estimates of the minimal coefficients in the inequality for each criterion and show that one of the calculated coefficients is exactly minimal. The obtained inequalities can be used for the acceleration of algorithms involving pairwise distances calculations between orbits. We present an algorithm for calculation of all distances not exceeding a fixed number in a quasi-metric space and demonstrate that the algorithm is faster than the complete calculation on the set of meteors orbits. Finally, we estimate the correlation dimensions of the set of main belt asteroids orbits and meteors orbits with respect to various orbital metrics and quasi-metrics.

KW - Clustering algorithm

KW - Correlation dimension

KW - Correlation integral

KW - Distance matrix

KW - Orbital similarity criterion

KW - Quasi-metric

KW - Relaxed triangle inequality

KW - Space of Keplerian orbits

KW - METEOR

KW - SEARCH

KW - EFFICIENT ALGORITHM

UR - http://www.scopus.com/inward/record.url?scp=85060731977&partnerID=8YFLogxK

U2 - 10.1007/s10569-019-9884-6

DO - 10.1007/s10569-019-9884-6

M3 - Article

AN - SCOPUS:85060731977

VL - 131

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 1

M1 - 5

ER -

ID: 39306249