Hyperbolicity of elliptic Lagrangian orbits in the planar three body problem |
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Authors: | YuWei Ou |
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Affiliation: | 1. Department of Mathematics, Shandong University, Jinan, 250100, China
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Abstract: | The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27(m 1 m 2 +m 2 m 3 +m 3 m 1)/(m 1 +m 2 +m 3)2 ∈ [0, 9] and the eccentricity e ∈ [0, 1). In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β > 8 with any eccentricity. |
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Keywords: | planar three-body problem Lagrangian solution hyperbolicity Maslov-type index |
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