title: Generating functions of the Cauchy operator of a hamiltonian system
metadata.name: dc.contributor.author
metadata.value: Shmyrov, Alexander S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shmyrov, Vasiliy A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shymanchuk, Dmitry V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-02-19T13:56:52Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-02-19T13:56:52Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Shmyrov A. S., Shmyrov V. A., Shymanchuk D. V. Generating functions of the Cauchy operator of a hamiltonian system. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 4, pp. 522–528. https://doi.org/10.21638/11701/spbu10.2023.408 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2023.408
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44909
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article is related to the mathematical apparatus for describing the phase trajectories
  of a hamiltonian system. An approach related to the construction of generating functions
  for the Cauchy operator is proposed. It is shown that one-parameter families of generating
  functions satisfy the Hamilton—Jacobi equation or its modifications. Using the example
  of small oscillations of a mathematical pendulum, it is shown that the description of the
  Cauchy operator for sufficiently long periods of time requires the use of generating functions
  of various types. With the help of generating functions, a variational principle similar to the
  principle of least action is formulated. The efficiency of using generating functions in the
  development of conservative methods of numerical integration is also noted.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was founded by the Russian Science Foundation (project N 23-21-00027,
  https://rscf.ru/project/23-21-00027/).
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. Applied Mathematics. Computer Science. Control Processes;Volume 19; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: hamilton equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generating function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Cauchy operator
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: variational principle
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Generating functions of the Cauchy operator of a hamiltonian system
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 08.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44909/1/08.pdf
resources.format: Adobe PDF
resources.size: 198,49 kB