论文标题
相等的欧拉相对平衡在s^2的旋转子午线上
Equal masses Eulerian relative equilibria on a rotating meridian of S^2
论文作者
论文摘要
确定了$ \ mathbb {s}^2 $在同等质量三体问题上的旋转子午线上的相对平衡。我们表明了鳞片和同步相对平衡的存在。除了两个相等的弧角$θ=π/2 $，几乎所有等同代三角形都可以形成相对平衡。对于$θ\在（0,2π/3）\ setMinus \ {π/2 \} $中，中质量必须在旋转轴上，在我们的情况下，在$ \ mathbb {s}^2 $的北极或南极。对于$θ\ in（2π/3，π）$，中质量必须在赤道上。对于$θ=2π/3 $，我们获得了等边三角形，其中质量的位置是任意的。当最大的ARC Angle $ a_ \ ell $在$ a_ \ ell \ in（π/2，a_c）$中，带有$ a_c = 1.8124 ... $，给定的$ a_ \ ell $存在两个scalene配置。
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 $a_\ell$.
