title: Geometry of the Huygens-Roche ﬁgure
metadata.name: dc.contributor.author
metadata.value: Kholshevnikov, Konstantin V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T10:04:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T10:04:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kholshevnikov K.V. Geometry of the Huygens—Roche figure. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 1, pp. 170– 176.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.113
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15547
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Theory of the ﬁgures of celestial bodies, which are in the state of hydrostatic equilibrium under gravitational, centrifugal, and pressure forces, took the form of a rigorous mathematical theory in the second part of the XX century. Fundamental physical laws served as its basis. The Huygens-Roche ﬁgure (total mass is concentrated in the centre, while the rotating atmosphere takes the equilibrium form) plays an important role in the theory. Properties of the ﬁgure are carefully examined. In particular, it is known that each isobar (surface of equal pressure) represents one of the three-parameter family of the Huygens- Roche surfaces. Meanwhile, convexity (or its absence) was not dicussed in the literature as far as we know. It is worth noting that there are non-convex ﬁgures between equilibrium ones. In the present paper, we ﬁnd the curvature of a meridional section of an arbitrary Huygens-Roche ﬁgure (in the closed form as well as in the form of a series in powers of the Clairaut parameter, main in the theory of equilibrium ﬁgures). We succeed to prove that the curvature is positive and is separated from zero. Hence, each surface from the Huygens-Roche ﬁgures family is convex, and has no points of ﬂattening. Moreover, no curve on its surface has points of straightening.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант № 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 6 (64); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: equilibrium figure
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Huygens—Roche figure
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: gravitational potential
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: curvature of a planar curve
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Geometry of the Huygens-Roche ﬁgure
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 170-176.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15547/1/170-176.pdf
resources.format: Adobe PDF
resources.size: 291,45 kB