title: Behaviour of the pendulum with a singular configuration space
metadata.name: dc.contributor.author
metadata.value: Burian, Sergey N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-12-27T13:53:50Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-12-27T13:53:50Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Burian S.N. Behaviour of the pendulum with a singular configuration space. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 4, pp. 541–551.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.402
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8799
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The flat double mathematical pendulum is considered, the loose end of which moves along an ellipse. In
  the general case, the configuration space of this pendulum is two disjoint curves. It is possible to choose
  parametres so that these curves intersect transversally. The observed trajectory of motion in this case
  forms an angle. Moreover, there are special parameters in which the curves have a first-order tangency.
  In this case, there is a geometric uncertainty  how the pendulum have to move after passing a singular
  point.
  It is shown that for the transversal case the inverse dynamic problem is not solvable, and the Lagrange
  multipliers tend to infinity as they move to a singular point in the configuration space. The observed motion
  is dynamically determined. The pendulum always moves from one branch of movement to another during
  the passage of a singular point. A qualitative explanation of this effect is proposed. Refs 11. Figs 3.
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 4(62); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: configuration spaces with singularities
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lagrange multipliers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: double pendulum
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Behaviour of the pendulum with a singular configuration space
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 02-Burian.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8799/1/02-Burian.pdf
resources.format: Adobe PDF
resources.size: 345,98 kB