Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem
Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem
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DOI：
10.1016/j.aim.2009.07.017
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发表时间：
2010-01
影响因子：
1.7
通讯作者：
Xijun Hu;Shanzhong Sun
中科院分区：
文献类型：
--
作者：
Xijun Hu;Shanzhong Sun
给出了一种研究天体力学稳定性问题的新方法。本文利用平面三体问题椭圆拉格朗日解的变分性质，利用哈密顿系统周期解的马斯洛夫型指标理论，研究了摩尔斯指数与其稳定性的关系。对于椭圆型拉格朗日解，我们用摩尔斯指数估计了其单矩阵单位特征值的代数多重性，这是理解稳定性问题的关键。作为一个特例，我们给出了相对平衡谱稳定性的判据。
We illustrate a new way to study the stability problem in celestial mechanics. In this paper, using the variational nature of elliptic Lagrangian solutions in the planar three-body problem, we study the relation between Morse index and its stability via Maslov-type index theory of periodic solutions of Hamiltonian system. For elliptic Lagrangian solutions we get an estimate of the algebraic multiplicity of unit eigenvalues of its monodromy matrix in terms of the Morse index, which is the key to understand the stability problem. As a special case, we provide a criterion to spectral stability of relative equilibrium.