Equal masses Eulerian relative equilibria on a rotating meridian of S^2
Relative equilibria on a rotating meridian on $\mathbb{S}^2$ in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles, including equilateral, can form a relative equilibrium, exce...
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ftdatacite:10.48550/arxiv.2203.14930 2023-05-15T18:22:25+02:00 Equal masses Eulerian relative equilibria on a rotating meridian of S^2 Fujiwara, Toshiaki Pérez-Chavela, Ernesto 2022 https://dx.doi.org/10.48550/arxiv.2203.14930 https://arxiv.org/abs/2203.14930 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Classical Analysis and ODEs math.CA FOS Mathematics 70F07, 70F15 Preprint Article article CreativeWork 2022 ftdatacite https://doi.org/10.48550/arxiv.2203.14930 2022-04-01T18:30:04Z Relative equilibria on a rotating meridian on $\mathbb{S}^2$ in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles, including equilateral, can form a relative equilibrium, except for the two equal arc angles $θ= π/2$. For $θ\in (0,2π/3)\setminus \{π/2\}$, the mid mass must be on the rotation axis, in our case, at the north or south pole of $\mathbb{S}^2$. For $θ\in (2π/3,π)$, the mid mass must be on the equator. For $θ=2π/3$, we obtain the equilateral triangle, where the position of the masses is arbitrary. When the largest arc angle $a_\ell$ is in $a_\ell\in (π/2,a_c)$, with $a_c=1.8124...$, two scalene configurations exist for given $a_\ell$. : 20 pages, 5 figures Report South pole DataCite Metadata Store (German National Library of Science and Technology) South Pole |
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DataCite Metadata Store (German National Library of Science and Technology) |
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topic |
Classical Analysis and ODEs math.CA FOS Mathematics 70F07, 70F15 |
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Classical Analysis and ODEs math.CA FOS Mathematics 70F07, 70F15 Fujiwara, Toshiaki Pérez-Chavela, Ernesto Equal masses Eulerian relative equilibria on a rotating meridian of S^2 |
topic_facet |
Classical Analysis and ODEs math.CA FOS Mathematics 70F07, 70F15 |
description |
Relative equilibria on a rotating meridian on $\mathbb{S}^2$ in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles, including equilateral, can form a relative equilibrium, except for the two equal arc angles $θ= π/2$. For $θ\in (0,2π/3)\setminus \{π/2\}$, the mid mass must be on the rotation axis, in our case, at the north or south pole of $\mathbb{S}^2$. For $θ\in (2π/3,π)$, the mid mass must be on the equator. For $θ=2π/3$, we obtain the equilateral triangle, where the position of the masses is arbitrary. When the largest arc angle $a_\ell$ is in $a_\ell\in (π/2,a_c)$, with $a_c=1.8124...$, two scalene configurations exist for given $a_\ell$. : 20 pages, 5 figures |
format |
Report |
author |
Fujiwara, Toshiaki Pérez-Chavela, Ernesto |
author_facet |
Fujiwara, Toshiaki Pérez-Chavela, Ernesto |
author_sort |
Fujiwara, Toshiaki |
title |
Equal masses Eulerian relative equilibria on a rotating meridian of S^2 |
title_short |
Equal masses Eulerian relative equilibria on a rotating meridian of S^2 |
title_full |
Equal masses Eulerian relative equilibria on a rotating meridian of S^2 |
title_fullStr |
Equal masses Eulerian relative equilibria on a rotating meridian of S^2 |
title_full_unstemmed |
Equal masses Eulerian relative equilibria on a rotating meridian of S^2 |
title_sort |
equal masses eulerian relative equilibria on a rotating meridian of s^2 |
publisher |
arXiv |
publishDate |
2022 |
url |
https://dx.doi.org/10.48550/arxiv.2203.14930 https://arxiv.org/abs/2203.14930 |
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South Pole |
geographic_facet |
South Pole |
genre |
South pole |
genre_facet |
South pole |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.2203.14930 |
_version_ |
1766201830097813504 |