Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на этот ресурс:
http://hdl.handle.net/11701/44909
Полная запись метаданных
Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Shmyrov, Alexander S. | - |
dc.contributor.author | Shmyrov, Vasiliy A. | - |
dc.contributor.author | Shymanchuk, Dmitry V. | - |
dc.date.accessioned | 2024-02-19T13:56:52Z | - |
dc.date.available | 2024-02-19T13:56:52Z | - |
dc.date.issued | 2023-12 | - |
dc.identifier.citation | 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) | en_GB |
dc.identifier.other | https://doi.org/10.21638/11701/spbu10.2023.408 | - |
dc.identifier.uri | http://hdl.handle.net/11701/44909 | - |
dc.description.abstract | 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. | en_GB |
dc.description.sponsorship | This work was founded by the Russian Science Foundation (project N 23-21-00027, https://rscf.ru/project/23-21-00027/). | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 19; Issue 4 | - |
dc.subject | hamilton equations | en_GB |
dc.subject | generating function | en_GB |
dc.subject | Cauchy operator | en_GB |
dc.subject | variational principle | en_GB |
dc.title | Generating functions of the Cauchy operator of a hamiltonian system | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 4 |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
---|---|---|---|---|
08.pdf | 198,49 kB | Adobe PDF | Просмотреть/Открыть |
Все ресурсы в архиве электронных ресурсов защищены авторским правом, все права сохранены.