title: Is Jacobi theorem valid in the singly averaged restricted circular Three-Body-Problem?
metadata.name: dc.contributor.author
metadata.value: Kholshevnikov, Konstantin V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T20:02:13Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T20:02:13Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kholshevnikov K.V. Is Jacobi theorem valid in the singly averaged restricted circular Three-Body-Problem? Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 179–184.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.116
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28446
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: C. Jacobi found that in the General N-Body-Problem (including N = 3) for the Lagrangian
  stability of any solution necessary is the negativity of the total energy of the system. For the
  restricted three-body-problem, this statement is trivial, since a zero-mass body introduces
  zero contribution to the energy of the system. If we consider only the equations describing
  the movement of the zero mass point, then the energy integral disappears. However, if we
  average the equations over the longitudes of the main bodies, the energy integral appears
  again. Is the Jacobi theorem valid in this case? It turned out not. For arbutrary large values
  of total energy, there exist bounded periodic orbits. At the same time the negative energy
  is sufficient for the boundedness of an orbit in the configuration space.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported my Russian Foundation for Basic Research (grant no. 18-02-00552).
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 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: restricted circular Three-Body-Problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Jacobi theorem on stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: averaging
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Is Jacobi theorem valid in the singly averaged restricted circular Three-Body-Problem?
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 179-184.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28446/1/179-184.pdf
resources.format: Adobe PDF
resources.size: 273,53 kB