title: Existence of liouvillian solutions in the problem of motion of a dynamically symmetric ball on a perfectly rough sphere
metadata.name: dc.contributor.author
metadata.value: Kuleshov, Alexander S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Katasonova, Vera A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:43:07Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:43:07Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kuleshov A. S., Katasonova V.A. Existence of liouvillian solutions in the problem of motion of a dynamically symmetric ball on a perfectly rough sphere. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 670–677.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.413
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15135
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of rolling without sliding of a rotationally symmetric rigid body on a sphere
  is considered. The rolling body is assumed to be subjected to the forces, the resultant of
  which is directed from the center of mass G of the body to the center O of the sphere, and
  depends only on the distance between G and O. In this case, the solution of this problem
  is reduced to solving the second-order linear differential equation over the projection of the
  angular velocity of the body onto its axis of symmetry. Using the Kovacic algorithm, we
  search for Liouvillian solutions of the corresponding second order linear differential equation.
  We prove that all solutions of this equation are Liouvillian in the case when the rolling
  rigid body is a nonhomogeneous dynamically symmetric ball. The paper is organized as
  follows. In the first paragraph, we briefly discuss the statement of the general problem of
  motion of a rotationally symmetric rigid on a perfectly rough sphere. We prove that this
  problem is reduced to solving the second order linear differential equation. In the second
  paragraph, we find Liouvillian solutions of this equation for the case, when the rolling rigid
  body is a dynamically symmetric ball.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (гранты №16-01-00338 и №17-01-00123).
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 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: body rolling on a sphere
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dynamically symmetric ball
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: Existence of liouvillian solutions in the problem of motion of a dynamically symmetric ball on a perfectly rough sphere
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 13-Kuleshov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15135/1/13-Kuleshov.pdf
resources.format: Adobe PDF
resources.size: 279,36 kB