The Non-Linear Stability of L4 in the Restricted Three-Body Problem when the Bigger Primary is a Triaxial Rigid Body期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Non-Linear Stability of L4 in the Restricted Three-Body Problem when the Bigger Primary is a Triaxial Rigid Body

Authors:

P P Hallan Sanjay Jain K B Bhatnagar

Institution:

(1) Department of Mathematics, Zakir Husain College, University of Delhi, Jawahar Lal Nehru Marg, New Delhi, 110002, India;(2) Department of Mathematics, University of Delhi, Delhi, 110007, India;(3) Centre for Fundamental Research in Space Dynamics and Celestial Mechanics, A-25, Rama Road, Adarsh Nagar, Delhi, 110033, India

Abstract:

The non-linear stability of L ₄ in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L ₄ is stable in the range of linear stability except for three mass ratios:

$\begin{gathered} \mu _{c1} = 0.242938971... - 0.17907...A_1 - 1.1774625...A_2 , \hfill \\ \mu _{c2} = 0.013516016... - 0.09938...A_1 - 2.15996...A_2 , \hfill \\ \mu _{c3} = 0.010936677... - 0.0294...A_1 + 772.85704...A_2 , \hfill \\ \end{gathered}$

where A₁, A₂ depend upon the lengths of the semi axes of the triaxial rigid body. This revised version was published online in July 2006 with corrections to the Cover Date.

Keywords:

restricted 3-body problem triaxial rigid body non-linear stability triangular point L ₄

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