title: Conical singular points and vector fields
metadata.name: dc.contributor.author
metadata.value: Burian, Sergei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-12-21T19:22:54Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-12-21T19:22:54Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Burian S. N. Conical singular points and vector fields. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 4, pp. 649–661.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.407
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/21916
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this article, several examples of mechanical systems which configuration spaces are smooth manifolds with a unique singular point are considered. Configuration spaces are the following: two smooth curves with a common point (or tangent) on the two-dimensional torus, four smooth curves on the four-dimensional torus with a common point, twodimensional cone (cusp) in the space R6. The main problem in the article is the calculation of (co)tangent space at a singular point by using different theoretical approaches. Outside of the singular point, the motion could be described in the frames of classical mechanics. But in the neighborhood of the singular points the terms like “tangent vector” and “cotangent vector” must have new conceptual definitions. In this article, the approach of differential spaces is used. Two differential structures for the modeling conical singular point are studied in order to construct (co)tangent space at singular points: locally-constants functions near to the cone vertex and the algebra of the restrictions of smooth functions in the comprehensive Euclidean space on the cone. In the first case, tangent and cotangent spaces at the singular points are zero. In the second case, the value of the functions on the cotangent bundle is constant on the cotangent layer under the singular point.
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 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: singular point
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: manifolds with conical singularities
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: differential spaces
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Conical singular points and vector fields
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 649-661.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/21916/1/649-661.pdf
resources.format: Adobe PDF
resources.size: 551,12 kB