Relative equilibria in curved restricted 4-and 5-body problems
Abstract We consider a 5-body problem on 2-dimensional surfaces of constant curvature κ , with four of the masses arranged at the vertices of a square and the fifth mass at the north pole of the sphere. The five-body set up is discussed for κ > 0 and for κ < 0. When the curvature is positive,...
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crioppubl:10.1088/1742-6596/1366/1/012006 2024-06-02T08:11:51+00:00 Relative equilibria in curved restricted 4-and 5-body problems Alhowaity, Sawsan Shoaib, Muhammad 2019 http://dx.doi.org/10.1088/1742-6596/1366/1/012006 https://iopscience.iop.org/article/10.1088/1742-6596/1366/1/012006/pdf https://iopscience.iop.org/article/10.1088/1742-6596/1366/1/012006 unknown IOP Publishing http://creativecommons.org/licenses/by/3.0/ https://iopscience.iop.org/info/page/text-and-data-mining Journal of Physics: Conference Series volume 1366, issue 1, page 012006 ISSN 1742-6588 1742-6596 journal-article 2019 crioppubl https://doi.org/10.1088/1742-6596/1366/1/012006 2024-05-07T13:56:09Z Abstract We consider a 5-body problem on 2-dimensional surfaces of constant curvature κ , with four of the masses arranged at the vertices of a square and the fifth mass at the north pole of the sphere. The five-body set up is discussed for κ > 0 and for κ < 0. When the curvature is positive, it is shown that relative equilibria exists when the four masses at the vertices of the square are either equal or two of them are infinitesimal such that it doesn’t effect the motion of the remaining three masses. However with two pairs of masses at the vertices of the square, no relative equilibria exists. In the hyperbolic case, κ < 0, there exist two values for the angular velocity which produce negative elliptic relative equilibria when the masses at the vertices of the square are equal. We also show that the solutions with non-equal masses do not exist in H 2 . Article in Journal/Newspaper North Pole IOP Publishing North Pole Journal of Physics: Conference Series 1366 1 012006 |
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Abstract We consider a 5-body problem on 2-dimensional surfaces of constant curvature κ , with four of the masses arranged at the vertices of a square and the fifth mass at the north pole of the sphere. The five-body set up is discussed for κ > 0 and for κ < 0. When the curvature is positive, it is shown that relative equilibria exists when the four masses at the vertices of the square are either equal or two of them are infinitesimal such that it doesn’t effect the motion of the remaining three masses. However with two pairs of masses at the vertices of the square, no relative equilibria exists. In the hyperbolic case, κ < 0, there exist two values for the angular velocity which produce negative elliptic relative equilibria when the masses at the vertices of the square are equal. We also show that the solutions with non-equal masses do not exist in H 2 . |
format |
Article in Journal/Newspaper |
author |
Alhowaity, Sawsan Shoaib, Muhammad |
spellingShingle |
Alhowaity, Sawsan Shoaib, Muhammad Relative equilibria in curved restricted 4-and 5-body problems |
author_facet |
Alhowaity, Sawsan Shoaib, Muhammad |
author_sort |
Alhowaity, Sawsan |
title |
Relative equilibria in curved restricted 4-and 5-body problems |
title_short |
Relative equilibria in curved restricted 4-and 5-body problems |
title_full |
Relative equilibria in curved restricted 4-and 5-body problems |
title_fullStr |
Relative equilibria in curved restricted 4-and 5-body problems |
title_full_unstemmed |
Relative equilibria in curved restricted 4-and 5-body problems |
title_sort |
relative equilibria in curved restricted 4-and 5-body problems |
publisher |
IOP Publishing |
publishDate |
2019 |
url |
http://dx.doi.org/10.1088/1742-6596/1366/1/012006 https://iopscience.iop.org/article/10.1088/1742-6596/1366/1/012006/pdf https://iopscience.iop.org/article/10.1088/1742-6596/1366/1/012006 |
geographic |
North Pole |
geographic_facet |
North Pole |
genre |
North Pole |
genre_facet |
North Pole |
op_source |
Journal of Physics: Conference Series volume 1366, issue 1, page 012006 ISSN 1742-6588 1742-6596 |
op_rights |
http://creativecommons.org/licenses/by/3.0/ https://iopscience.iop.org/info/page/text-and-data-mining |
op_doi |
https://doi.org/10.1088/1742-6596/1366/1/012006 |
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Journal of Physics: Conference Series |
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1366 |
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1 |
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012006 |
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1800758126422523904 |