title: Zero velocity surface in the general three-body-problem
metadata.name: dc.contributor.author
metadata.value: Titov, Vladimir B.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-17T09:44:50Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-17T09:44:50Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Titov V.B. Zero velocity surface in the general three-body-problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 1, pp. 165–175. https://doi.org/10.21638/spbu01.2023.114 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.114
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39337
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The zero-velocity surfaces of the general planar three-body problem are constructed in the
  form space, the factor-space of the configuration space by transfer and rotation. Such a
  space is the space of congruent triangles, and the sphere in this space is similar triangles.
  The integral of energy in the form space gives the equation of the zero velocity surface. These
  surfaces can also be obtained based on the Sundman inequality. Such surfaces separate areas
  of possible movement from areas where movement is impossible. Without loss of generality,
  we can assume that the constant energy is −1/2 and the sought for surfaces depend only
  on the magnitude of the angular momentum of the problem, J. Depending on this value,
  five topologically different types of surfaces can be distinguished. For small J, the surface
  consists of two separate surfaces, internal and external ones, the motion is possible only
  between them. With J increasing the inner surface increases, the outer surface decreases,
  the surfaces first have a common point at some value of J, with a further increasing of J,
  their topological type changes and finally the zero-velocity surface splits into three disjoint
  surfaces, the motion is possible only inside them. Examples of the corresponding surfaces
  are given for each of these types, their sections in the plane xy and in the plane xz and the
  surfaces themselves are constructed, their properties are studied.
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 10 (68); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: general three-body-problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: zero velocity surface
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: region of feasibility
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Zero velocity surface in the general three-body-problem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15502-Текст статьи-51853-1-2-20230304.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39337/1/15502-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-51853-1-2-20230304.pdf
resources.format: Adobe PDF
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