Bogolyubov averaging and normalization procedures in nonlinear mechanics. II
By using a new method suggested in the first part of the present work, we study systems which become linear in the zero approximation and have perturbations in the form of polynomials. This class of systems has numerous applications. The following fact is even more important: Our technique demonstra...
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| Datum: | 1994 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5590 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511819862376448 |
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| author | Lopatin, A. K. Mitropolskiy, Yu. A. Лопатін, А. К. Митропольський, Ю. О. |
| author_facet | Lopatin, A. K. Mitropolskiy, Yu. A. Лопатін, А. К. Митропольський, Ю. О. |
| author_sort | Lopatin, A. K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:14:13Z |
| description | By using a new method suggested in the first part of the present work, we study systems which become linear in the zero approximation and have perturbations in the form of polynomials. This class of systems has numerous applications. The following fact is even more important: Our technique demonstrates how to generalize the classical method of Poincaré-Birkhoff normal forms and obtain new results by using group-theoretic methods. After a short exposition of the general theory of the method of asymptotic decomposition, we illustrate the new normalization technique as applied to models based on the Lotka-Volterra equations. |
| first_indexed | 2026-03-24T03:18:57Z |
| format | Article |
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| id | umjimathkievua-article-5590 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:18:57Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/02/4b8910fcb6e6872d4f27dbefe0e5eb02.pdf |
| spelling | umjimathkievua-article-55902020-03-19T09:14:13Z Bogolyubov averaging and normalization procedures in nonlinear mechanics. II Bogolyubov averaging and normalization procedures in nonlinear mechanics. II Lopatin, A. K. Mitropolskiy, Yu. A. Лопатін, А. К. Митропольський, Ю. О. By using a new method suggested in the first part of the present work, we study systems which become linear in the zero approximation and have perturbations in the form of polynomials. This class of systems has numerous applications. The following fact is even more important: Our technique demonstrates how to generalize the classical method of Poincaré-Birkhoff normal forms and obtain new results by using group-theoretic methods. After a short exposition of the general theory of the method of asymptotic decomposition, we illustrate the new normalization technique as applied to models based on the Lotka-Volterra equations. За допомогою нового методу досліджуються системи, лінійні у нульовому наближенні, що мають збурення у формі поліномів. Цей клас систем має широке застосування. Однак більш значним є той факт, що новий метод показує, як можна узагальнити класичний метод нормальної форми Пуанкаре-Біркгофа і як можуть бути одержані нові результати завдяки застосуванню теоретико-групового апарату. Після стислого викладення загальної теорії ілюструється техніка нормалізації за методом асимптотичної декомпозиції на моделях, заснованих на рівняннях Лотке-Вольтерра. Institute of Mathematics, NAS of Ukraine 1994-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5590 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 11 (1994); 1509–1526 Український математичний журнал; Том 46 № 11 (1994); 1509–1526 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5590/7865 https://umj.imath.kiev.ua/index.php/umj/article/view/5590/7866 Copyright (c) 1994 Lopatin A. K.; Mitropolskiy Yu. A. |
| spellingShingle | Lopatin, A. K. Mitropolskiy, Yu. A. Лопатін, А. К. Митропольський, Ю. О. Bogolyubov averaging and normalization procedures in nonlinear mechanics. II |
| title | Bogolyubov averaging and normalization procedures in nonlinear mechanics. II |
| title_alt | Bogolyubov averaging and normalization procedures in nonlinear mechanics. II |
| title_full | Bogolyubov averaging and normalization procedures in nonlinear mechanics. II |
| title_fullStr | Bogolyubov averaging and normalization procedures in nonlinear mechanics. II |
| title_full_unstemmed | Bogolyubov averaging and normalization procedures in nonlinear mechanics. II |
| title_short | Bogolyubov averaging and normalization procedures in nonlinear mechanics. II |
| title_sort | bogolyubov averaging and normalization procedures in nonlinear mechanics. ii |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5590 |
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