title: Liouvillian solutions in the problem of rolling of a heavy homogeneous ball on a surface of revolution
metadata.name: dc.contributor.author
metadata.value: Kuleshov, Alexander S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Solomina, Darya V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-02-16T19:36:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-02-16T19:36:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kuleshov A. S., Solomina D.V. Liouvillian solutions in the problem of rolling of a heavy homogeneous ball on a surface of revolution. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 4, pp. 653–660.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.411
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/35113
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of rolling without sliding of a homogeneous ball on a fixed surface under the
  action of gravity is a classical problem of nonholonomic system dynamics. Usually, when
  considering this problem, following the E. J.Routh approach it is convenient to define explicitly
  the equation of the surface, on which the ball’s centre is moving. This surface is
  equidistant to the surface, over which the contact point is moving. From the classical works
  of E. J. Routh and F. Noether it was known that if the ball rolls on a surface such that its
  centre moves along a surface of revolution, then the problem is reduced to solving the second
  order linear differential equation. Therefore it is interesting to study for which surface
  of revolution the corresponding second order linear differential equation admits Liouvillian
  solutions. To solve this problem it is possible to apply the Kovacic algorithm to the corresponding
  second order linear differential equation. In this paper we present our own method
  to derive the corresponding second order linear differential equation. In the case when the
  centre of the ball moves along the ellipsoid of revolution we prove that the corresponding
  second order linear differential equation admits a liouvillian solution.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by Russian Foundation for Basic Research (grants no. 19-01-00140 and
  20-01-00637).
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 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: rolling without sliding
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: homogeneous ball
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: surface of revolution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Kovacic algorithm
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Liouvillian solutions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Liouvillian solutions in the problem of rolling of a heavy homogeneous ball on a surface of revolution
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 653-660.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/35113/1/653-660.pdf
resources.format: Adobe PDF
resources.size: 282,26 kB