title: On a quotient space of Keplerian orbits
metadata.name: dc.contributor.author
metadata.value: Kholshevnikov, Konstantin V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shchepalova, Anastassia S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Jazmati, Mohammad S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T13:40:07Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T13:40:07Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kholshevnikov K.V., Shchepalova A. S., Jazmati M. S. On a quotient space of Keplerian orbits. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 165–174.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.116
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17339
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Several metrics were proposed during last 15 years which transform divers spaces of Keplerian
  orbits in metric ones. They are used to estimate a proximity of orbits of celestial
  bodies (usually comets, asteroids, and meteoroid complexes). An important role play quotient
  spaces. They allow us not to take into account those orbital elements which change in
  the secular mode under different perturbations. Three quotient spaces were just examined.
  Nodes are ignored in one of them; arguments of pericenters are ignored in the second one;
  both nodes and arguments of pericenters are ignored in the third one. Here, we introduce
  a fourth quotient space where orbits with arbitrary longitudes of nodes and arguments of
  pericenters are identified under the condition that their sum (longitude of pericenter) is
  fixed. The function ̺6 serving as a distance between pointed classes of orbits, and satisfying
  first two axioms of metric spaces is determined. An algorithm of its calculation is
  proposed. In general the most complicated part of the algorithm represents the solution of
  a trigonometric equation of third degree. The question on the validity of the triangle axiom
  for ̺6, at least in a relaxed variant, will be examined later.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: Keplerian orbit
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: metrics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quotient space of a metric space
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: distance between orbits
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On a quotient space of Keplerian orbits
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 165-174.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17339/1/165-174.pdf
resources.format: Adobe PDF
resources.size: 308,98 kB