On a particular case of motion in the three-body problem
UDC 531.36; 531.011 We study the three-body problem in a particular case where two bodies have equal masses, which implies the existence of a manifold of symmetric motions. We are looking for the conditions of existence of bounded (unbounded) symmetric motions.Our analysis of boundedness (unboundedn...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6756 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865793600585990144 |
|---|---|
| author | Sosnyts’kyi , S. P. Сосницький, С. П. |
| author_facet | Sosnyts’kyi , S. P. Сосницький, С. П. |
| author_institution_txt_mv | [
{
"author": "С. П. Сосницький",
"institution": "Iн-т математики НАН України, Київ"
}
] |
| author_sort | Sosnyts’kyi , S. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-02-10T11:32:00Z |
| description | UDC 531.36; 531.011
We study the three-body problem in a particular case where two bodies have equal masses, which implies the existence of a manifold of symmetric motions. We are looking for the conditions of existence of bounded (unbounded) symmetric motions.Our analysis of boundedness (unboundedness) of motions shows that both the structure of the manifold of symmetrical motions and the integrals of energy and angular momentum are essential. |
| doi_str_mv | 10.37863/umzh.v73i10.6756 |
| first_indexed | 2026-03-24T03:29:59Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6756 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:29:59Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-67562026-02-10T11:32:00Z On a particular case of motion in the three-body problem ОБ ОДНОМ ЧАСТНОМ СЛУЧАЕ ДВИЖЕНИЯ В ЗАДАЧЕ ТРЕХ ТЕЛ Про один окремий випадок руху в задачі трьох тіл Sosnyts’kyi , S. P. Сосницький, С. П. Симетричний рух Symmetrical motion, a Hill stable pair, distal motion, bounded motion UDC 531.36; 531.011 We study the three-body problem in a particular case where two bodies have equal masses, which implies the existence of a manifold of symmetric motions. We are looking for the conditions of existence of bounded (unbounded) symmetric motions.Our analysis of boundedness (unboundedness) of motions shows that both the structure of the manifold of symmetrical motions and the integrals of energy and angular momentum are essential. Исследуется  частный случай  задачи  трех  тел, когда  два из них имеют  одинаковые массы, что  обусловливает существование многообразия  симметричных движений. Рассматриваются  условия существования ограниченных (неограниченных) симметричных движений. Для анализа  ограниченности (неограниченности) движения являются существенными как  структура многообразия симметричных движений, так и  интегралы энергии и  момента количеств движения. УДК 531.36; 531.011Дослiджується окремий випадок задачi трьох тiл, коли два з них мають однаковi маси, що обумовлює iснування многовиду симетричних рухiв. Розглянуто умови iснування обмежених (необмежених) симетричних рухiв. Для аналiзу обмеженостi (необмеженостi) руху як структура многовиду симетричних рухiв, так i iнтеграли енергiї та моменту кiлькостей руху є iстотними. Institute of Mathematics, NAS of Ukraine 2026-02-09 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/6756 10.37863/umzh.v73i10.6756 Ukrains’kyi Matematychnyi Zhurnal; Vol. 73 No. 10 (2021); 1404-1413 Український математичний журнал; Том 73 № 10 (2021); 1404-1413 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/6756/9123 Copyright (c) 2021 Stepan |
| spellingShingle | Sosnyts’kyi , S. P. Сосницький, С. П. On a particular case of motion in the three-body problem |
| title | On a particular case of motion in the three-body problem |
| title_alt | ОБ ОДНОМ ЧАСТНОМ СЛУЧАЕ ДВИЖЕНИЯ В ЗАДАЧЕ ТРЕХ ТЕЛ Про один окремий випадок руху в задачі трьох тіл |
| title_full | On a particular case of motion in the three-body problem |
| title_fullStr | On a particular case of motion in the three-body problem |
| title_full_unstemmed | On a particular case of motion in the three-body problem |
| title_short | On a particular case of motion in the three-body problem |
| title_sort | on a particular case of motion in the three-body problem |
| topic_facet | Симетричний рух Symmetrical motion a Hill stable pair distal motion bounded motion |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6756 |
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