Stability and bifurcations of the figure-8 solution of the three-body problem.
Stability and bifurcations of the figure-8 solution of the three-body problem.
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DOI：
10.1103/physrevlett.88.241101
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发表时间：
2002-05
影响因子：
8.6
通讯作者：
J. Galán;F. Muñoz-Almaraz;E. Freire;E. Doedel;A. Vanderbauwhede
中科院分区：
文献类型：
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作者：
J. Galán;F. Muñoz-Almaraz;E. Freire;E. Doedel;A. Vanderbauwhede
本文分析了最近发现的具有等质量和8字形的一般三体问题解随质量变化时的稳定性。通过数值延拓和特征乘子的计算表明，该解仅在较窄的质量区间内是稳定的。在与8号轨道相同的同伦类中，还发现了其他不对称的、质量相等的不稳定解。并对分支行为进行了分析。
The stability properties of a recently discovered solution of the general three-body problem with equal masses and the shape of a figure 8 are analyzed as the masses are varied. It is shown by numerical continuation and the evaluation of the characteristic multipliers that the solution is stable only in a narrow mass interval. Other less symmetrical and unstable solutions with equal masses in the same homotopy class as the figure-8 orbit have been found. The branching behavior is also analyzed.