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...
| Main Authors: | , |
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| Format: | Report |
| Language: | unknown |
| Published: |
arXiv
2022
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2203.14930 https://arxiv.org/abs/2203.14930 |
| Summary: | 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 |
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