The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problem
The study of central configurations, whose concepts and definitions were already formulated by the classics of celestial mechanics - Euler, Lagrange, Laplace and Liouville in the XVIII-XIX centuries, is of interest not only for celestial mechanics, but also for many sections of mathematical analysis...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2023-12-01
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| Series: | RUDN Journal of Engineering Research |
| Subjects: | |
| Online Access: | https://journals.rudn.ru/engineering-researches/article/viewFile/37373/22993 |
| _version_ | 1797358808454922240 |
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| author | Yulianna V. Perepelkina Alexander N. Zadiranov |
| author_facet | Yulianna V. Perepelkina Alexander N. Zadiranov |
| author_sort | Yulianna V. Perepelkina |
| collection | DOAJ |
| description | The study of central configurations, whose concepts and definitions were already formulated by the classics of celestial mechanics - Euler, Lagrange, Laplace and Liouville in the XVIII-XIX centuries, is of interest not only for celestial mechanics, but also for many sections of mathematical analysis, differential equations, analytical mechanics, stellar dynamics and space flight dynamics. In recent decades, there have been opportunities to use the concept of central configurations also in theoretical physics, chemistry, crystallography, etc. We consider planar central configurations, called nested, consisting of polygons sequentially nested one into another, at the vertices of which there are bodies (material points). The existence of nested planar central configurations of trapezoidal type with a sphere in the centre is proved. Early, it was found that abovementioned isolated central configurations exist in the heliocentric rotated coordinate systems. It was supposed only the Newton’s law of attraction is acting between bodies. The Maple software is used to derive the solution of this problem. |
| first_indexed | 2024-03-08T15:06:31Z |
| format | Article |
| id | doaj.art-9a6ea2600b2d491b98bab125e68c8981 |
| institution | Directory Open Access Journal |
| issn | 2312-8143 2312-8151 |
| language | English |
| last_indexed | 2024-03-08T15:06:31Z |
| publishDate | 2023-12-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | RUDN Journal of Engineering Research |
| spelling | doaj.art-9a6ea2600b2d491b98bab125e68c89812024-01-10T14:57:41ZengPeoples’ Friendship University of Russia (RUDN University)RUDN Journal of Engineering Research2312-81432312-81512023-12-0124434034810.22363/2312-8143-2023-24-4-340-34821106The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problemYulianna V. Perepelkina0https://orcid.org/0000-0001-8115-8253Alexander N. Zadiranov1https://orcid.org/0000-0001-7787-8290Russian Institute for Scientific and Technical Information of Russian Academy of SciencesState Fire Academy of EMERCOM of RussiaThe study of central configurations, whose concepts and definitions were already formulated by the classics of celestial mechanics - Euler, Lagrange, Laplace and Liouville in the XVIII-XIX centuries, is of interest not only for celestial mechanics, but also for many sections of mathematical analysis, differential equations, analytical mechanics, stellar dynamics and space flight dynamics. In recent decades, there have been opportunities to use the concept of central configurations also in theoretical physics, chemistry, crystallography, etc. We consider planar central configurations, called nested, consisting of polygons sequentially nested one into another, at the vertices of which there are bodies (material points). The existence of nested planar central configurations of trapezoidal type with a sphere in the centre is proved. Early, it was found that abovementioned isolated central configurations exist in the heliocentric rotated coordinate systems. It was supposed only the Newton’s law of attraction is acting between bodies. The Maple software is used to derive the solution of this problem.https://journals.rudn.ru/engineering-researches/article/viewFile/37373/22993celestial mechanicsmaple softwarenested configurationstrapezoidal configurationsspherical central body |
| spellingShingle | Yulianna V. Perepelkina Alexander N. Zadiranov The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problem RUDN Journal of Engineering Research celestial mechanics maple software nested configurations trapezoidal configurations spherical central body |
| title | The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problem |
| title_full | The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problem |
| title_fullStr | The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problem |
| title_full_unstemmed | The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problem |
| title_short | The nested planar central configurations of a trapezoid form in classical and generalized versions of the general (4n+1)-body problem |
| title_sort | nested planar central configurations of a trapezoid form in classical and generalized versions of the general 4n 1 body problem |
| topic | celestial mechanics maple software nested configurations trapezoidal configurations spherical central body |
| url | https://journals.rudn.ru/engineering-researches/article/viewFile/37373/22993 |
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