title: The space of Keplerian orbits and a family of its quotient spaces
metadata.name: dc.contributor.author
metadata.value: Kholshevnikov, Konstantin V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Milanov, Danila V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shchepalova, Anastasia S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-07-16T16:53:38Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-07-16T16:53:38Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kholshevnikov K.V., Milanov D.V., Shchepalova A. S. The space of Keplerian orbits and a family of its quotient spaces. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 2, pp. 359–369.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.215
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/29891
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Distance functions on the set of Keplerian orbits play an important role in solving problems
  of searching for parent bodies of meteoroid streams. A special kind of such functions are
  distances in the quotient spaces of orbits. Three metrics of this type were developed earlier.
  These metrics allow to disregard the longitude of ascending node or the argument of
  pericenter or both. Here we introduce one more quotient space, where two orbits are considered
  identical if they differ only in their longitudes of nodes and arguments of pericenters,
  but have the same sum of these elements (the longitude of pericenter). The function ̺6 is
  defined to calculate distance between two equivalence classes of orbits. The algorithm for
  calculation of ̺6 value is provided along with a reference to the corresponding program,
  written in C++ language. Unfortunately, ̺6 is not a full-fledged metric. We proved that
  it satisfies first two axioms of metric space, but not the third one: the triangle inequality
  does not hold, at least in the case of large eccentricities. However there are two important
  particular cases when the triangle axiom is satisfied: one of three orbits is circular, longitudes
  of pericenters of all three orbits coincide. Perhaps the inequality holds for all elliptic
  orbits, but this is a matter of future research.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by Russian Science Foundation (grant no. 18-12-00050).
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 8 (66); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: Keplerian orbit
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: metric
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quotient space of 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: The space of Keplerian orbits and a family of its quotient spaces
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 359-369.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/29891/1/359-369.pdf
resources.format: Adobe PDF
resources.size: 349,45 kB