Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem

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...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 223; no. 1; pp. 98 - 119
Main Authors Hu, Xijun, Sun, Shanzhong
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2010
Subjects
Lagrangian solution
Linear stability
Maslov-type index
Morse index
Planar three-body problem
Linear stability
Morse index
Planar three-body problem
Lagrangian solution
Maslov-type index
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2009.07.017