Families of symmetric relative periodic orbits originating from the circular Euler solution in the isosceles three body problem
Families of symmetric relative periodic orbits originating from the circular Euler solution in the isosceles three body problem
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源于等腰三体问题中圆欧拉解的对称相对周期轨道族
DOI：
10.1007/s10569-011-9338-2
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发表时间：
2011
影响因子：
1.6
通讯作者：
M. Shibayama and K. Yagasaki
中科院分区：
文献类型：
--
作者：
Fumihiko Hirosawa;Tang Bao Ngoc Bui;K.Aoyama;M. Shibayama and K. Yagasaki
我们使用理论和数值方法研究等腰三体问题中的对称相对周期轨道。我们首先证明除了椭圆欧拉解之外，圆形欧拉解还诞生了另一族对称相对周期轨道。先前的研究还表明，存在无限多个对称相对周期轨道族，这些轨道是由三重碰撞之间的异宿连接以及二元碰撞的平面周期轨道之间产生的。我们对对称相对周期轨道进行了数值延拓分析，并观察到从圆形欧拉解所产生的两个系列中分叉出来的丰富的对称相对周期轨道系列。随着角动量趋于零，许多数值观测的族收敛到三重碰撞或平面周期轨道与先前结果中描述的二元碰撞之间的异宿连接，而其中一些收敛到平面问题中“以前未知”的周期轨道。
We study symmetric relative periodic orbits in the isosceles three-body problem using theoretical and numerical approaches. We first prove that another family of symmetric relative periodic orbits is born from the circular Euler solution besides the elliptic Euler solutions. Previous studies also showed that there exist infinitely many families of symmetric relative periodic orbits which are born from heteroclinic connections between triple collisions as well as planar periodic orbits with binary collisions. We carry out numerical continuation analyses of symmetric relative periodic orbits, and observe abundant families of symmetric relative periodic orbits bifurcating from the two families born from the circular Euler solution. As the angular momentum tends to zero, many of the numerically observed families converge to heteroclinic connections between triple collisions or planar periodic orbits with binary collisions described in the previous results, while some of them converge to “previously unknown” periodic orbits in the planar problem.