title: Dynamics of a double pendulum with viscous friction in the joints. I. Mathematical model of motion and construction of the regime diagram
metadata.name: dc.contributor.author
metadata.value: Smirnov, Alexey S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kravchinskiy, Igor A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-07-04T12:44:25Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-07-04T12:44:25Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Smirnov A. S., Kravchinskiy I. A. Dynamics of a double pendulum with viscous friction in the joints. I. Mathematical model of motion and construction of the regime diagram. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, vol. 11 (69), issue 2, pp. 371–384. https://doi.org/10.21638/spbu01.2024.210 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2024.210
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/45702
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper discusses the dynamic behavior of a double mathematical pendulum with
  identical parameters of links and end loads, which is under the influence of viscous friction
  in both of its joints with generally different dissipative coefficients. A linear mathematical
  model of the system motion for small deviations is given, and a characteristic equation containing two dimensionless dissipative parameters is derived. For the case of low damping,
  approximate analytical expressions are found that make it possible to evaluate and compare
  with each other the damping factors during the motion of the system on each of the
  oscillation modes. A diagram of dissipative motion regimes is constructed, which arises
  when the plane of dimensionless parameters is divided by discriminant curves into regions
  with a qualitatively different character of the system motion. It is noted that a dissipative
  internal resonance can take place in the system under consideration, and the conditions for
  its existence in an analytical form are established, as well as their graphic illustration is
  also given. This article is the first part of the study of the dynamics of a dissipative double
  pendulum, the continuation of which will be presented as a separate work “Dynamics of a
  double pendulum with viscous friction in the joints. II. Dissipative oscillation modes and
  optimization of damping parameters”.
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 11 (69); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: double pendulum
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: viscous damping
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: low friction
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: damping factor
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: discriminant curve
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dissipative regime diagram
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dissipative internal resonance
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Dynamics of a double pendulum with viscous friction in the joints. I. Mathematical model of motion and construction of the regime diagram
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 371-384.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/45702/1/371-384.pdf
resources.format: Adobe PDF
resources.size: 443,56 kB