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

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

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.

Язык оригиналаанглийский
Номер статьи5
ЖурналCelestial Mechanics and Dynamical Astronomy
Том131
Номер выпуска1
DOI
СостояниеОпубликовано - 1 янв 2019

Отпечаток

Triangle inequality
triangles
Orbits
Orbit
meteor
orbits
orbitals
meteoroids
eccentricity
asteroid
Quasi-metric
Quasi-metric Space
metric space
asteroid belts
Asteroids
Correlation Dimension
Eccentricity
Coefficient
coefficients
estimates

Предметные области Scopus

  • Астрономия и астрофизика
  • Моделирование и симуляция
  • Вычислительная математика
  • Прикладная математика

Цитировать

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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.",
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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.

Результат исследований: Научные публикации в периодических изданияхстатья

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

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