Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem
Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem
复制标题
Robe受限椭圆三体问题平衡点线性稳定性的解析结果
DOI：
10.3934/dcds.2017074
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发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
张永超
中科院分区：
文献类型：
--
作者：
周青龙;张永超
研究了长袍的限制性三体问题。这种运动首先由A. G.长袍在[ 13 ]，这是用来模拟小振荡的地球内核考虑到月球的吸引力。关于长袍限制问题中椭圆平衡点的线性稳定性，以往的结果依赖于大量的数值计算，本文给出了一种解析方法，在我们的问题中，椭圆平衡点附近的线性化哈密顿系统与经典三体问题中欧拉椭圆相对平衡点附近的线性化哈密顿系统，除了质量参数的取值范围不同外，是一致的。我们首先建立了线性稳定性问题与辛路及相应线性算子的性质之间的关系。然后利用辛路径的Maslov型\开始{document} $ω$ \end{document} -指标理论和线性算子理论，计算了\开始{document} $ω$ \end{document} -指标，得到了长袍约束三体问题椭圆平衡点线性稳定性的若干性质.
We study the Robe's restricted three-body problem. Such a motion was firstly studied by A. G. Robe in [ 13 ], which is used to model small oscillations of the earth's inner core taking into account the moon's attraction. Earlier results for the linear stability of the elliptic equilibrium point in Robe's restricted problem depend on a lot of numerical computations, while we give an analytic approach to it. The linearized Hamiltonian system near the elliptic equilibrium point in our problem coincides with the linearized system near the Euler elliptic relative equilibria in the classical three-body problem except for the range of the mass parameter. We first establish some relations of the linear stability problem to the properties of some symplectic paths and some corresponding linear operators. Then using the Maslov-type \begin{document} $ω$ \end{document} -index theory of symplectic paths and the theory of linear operators, we compute \begin{document} $ω$ \end{document} -indices and obtain certain properties of the linear stability of the elliptic equilibrium point of Robe's restricted three-body problem.
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DOI：
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