First steps towards the averaging with respect to a part of the coordinates
The problem of averaging on an infinite time interval is considered. The classical results on averaging proved by N.N. Bogoluybov are generalized to the case in which only a part of the coordinates in the phase space remains close to the equilibrium position of the averaged system. We call...
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| Format: | Article |
| Language: | English |
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Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2025-01-01
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| Series: | Theoretical and Applied Mechanics |
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| Online Access: | https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500005P.pdf |
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| _version_ | 1849245180421472256 |
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| author | Polekhin Ivan |
| author_facet | Polekhin Ivan |
| author_sort | Polekhin Ivan |
| collection | DOAJ |
| description | The problem of averaging on an infinite time interval is considered. The
classical results on averaging proved by N.N. Bogoluybov are generalized to
the case in which only a part of the coordinates in the phase space remains
close to the equilibrium position of the averaged system. We call this the
averaging with respect to a part of the coordinates. The results are based
on some topological ideas combined with the standard theorem on averaging on
a finite time interval. |
| format | Article |
| id | doaj-art-d9b1dbf2ed234a7a9ef6b38c7b963ee5 |
| institution | Kabale University |
| issn | 1450-5584 2406-0925 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade |
| record_format | Article |
| series | Theoretical and Applied Mechanics |
| spelling | doaj-art-d9b1dbf2ed234a7a9ef6b38c7b963ee52025-08-20T03:58:54ZengSerbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, BelgradeTheoretical and Applied Mechanics1450-55842406-09252025-01-0152111512510.2298/TAM250110005P1450-55842500005PFirst steps towards the averaging with respect to a part of the coordinatesPolekhin Ivan0https://orcid.org/0009-0008-4979-8144Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia + Moscow Institute of Physics and Technology, Dolgoprudny, Russia + Lomonosov Moscow State University, Moscow, Russia + P.G. Demidov Yaroslavl State University, Yaroslavl, RussiaThe problem of averaging on an infinite time interval is considered. The classical results on averaging proved by N.N. Bogoluybov are generalized to the case in which only a part of the coordinates in the phase space remains close to the equilibrium position of the averaged system. We call this the averaging with respect to a part of the coordinates. The results are based on some topological ideas combined with the standard theorem on averaging on a finite time interval.https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500005P.pdfperiodic systemsaveragingrapid oscillationsinfinite time intervaltopological methods in dynamics. |
| spellingShingle | Polekhin Ivan First steps towards the averaging with respect to a part of the coordinates Theoretical and Applied Mechanics periodic systems averaging rapid oscillations infinite time interval topological methods in dynamics. |
| title | First steps towards the averaging with respect to a part of the coordinates |
| title_full | First steps towards the averaging with respect to a part of the coordinates |
| title_fullStr | First steps towards the averaging with respect to a part of the coordinates |
| title_full_unstemmed | First steps towards the averaging with respect to a part of the coordinates |
| title_short | First steps towards the averaging with respect to a part of the coordinates |
| title_sort | first steps towards the averaging with respect to a part of the coordinates |
| topic | periodic systems averaging rapid oscillations infinite time interval topological methods in dynamics. |
| url | https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500005P.pdf |
| work_keys_str_mv | AT polekhinivan firststepstowardstheaveragingwithrespecttoapartofthecoordinates |