title: Reaction forces of singular pendulum
metadata.name: dc.contributor.author
metadata.value: Burian, Sergei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-07-07T21:41:37Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-07-07T21:41:37Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Burian S. N. Reaction forces of singular pendulum. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 2, pp. 278–293.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.209
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/37107
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Various behavior types of reaction forces and Lagrange multipliers for the case of mechanical
  systems with configuration space singularities are studied in this paper. The motion of
  a one-dimensional double pendulum (or a singular pendulum) with a transversal singular
  point or a first order tangency singular point is considered. Properties of the configuration
  space of singular pendulum depends on the constraint line which the free vertex of
  the double pendulum moves along. Configuration space of singular pendulum could be
  represented by two smooth curves on a torus without common points, two transversely
  intersecting smooth curves or two curves with first-order tangency. In order to study the
  pendulum motion, the reaction forces on a two-dimensional torus are found. The expressions
  for the reaction forces are obtained analytically in angular coordinates. In the case
  of a transverse intersection it is proved that the reaction forces must be zero at the singular
  point. In the case of a first-order tangency singularity, the reaction forces are nonzero
  at the singular point. The Lagrange multiplier which depends on the motion along the
  ellipse becomes unlimited near to the singular point. Two mechanisms with a different
  type of singular points in the configuration space are described: a nonsmooth singular
  pendulum and a broken singular pendulum. There are no smooth regular curves passing
  through a singular point in the configuration spaces of these mechanical systems. In the
  case of nonsmooth singular pendulum, the Lagrange multiplier which depends on the motion
  along the ellipse becomes undefined when the singular point is passed. In the case of
  broken singular pendulum, the Lagrange multiplier makes a jump from a finite value to an
  infinite one.
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 9 (67); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: singular point
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: holonomic constraint
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lagrange multipliers
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Reaction forces of singular pendulum
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 278-293.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/37107/1/278-293.pdf
resources.format: Adobe PDF
resources.size: 562,48 kB