Variational Minimizing Solutions for Planar Circular Restricted 3-Body Problems

Zhang Shiqing

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Variational Minimizing Solutions for Planar Circular Restricted 3-Body Problems

Zhang Shiqing *

Sichuan University

*Correspondence author

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Funding: 国家自然科学基金,教育部博士点基金（No.,）

Opened online: 3 March 2009

Accepted by: none

Citation: Zhang Shiqing.Variational Minimizing Solutions for Planar Circular Restricted 3-Body Problems[OL]. [ 3 March 2009] http://en.paper.edu.cn/en_releasepaper/content/29855

We use some inequalities to study planar Newtonian circular restricted 3- body problems with two equal primaries, we prove that the minimizer of the Lagrangian action on “8” type symmetric loop spaces of the rotational coordinate systems is just at the center of masses, which implies that we must add topological conditions in order to get the true “8”–type solutions.

Keywords:Restricted 3–body problems;“8” type loops;Variational methods

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