Symmetry of planar four-body convex central configurations

被引：60

作者：

Albouy, Alain ^{[1
]}

Fu, Yanning ^{[2
]}

Sun, Shanzhong ^{[3
]}

机构：

[1] Observ Paris, CNRS, UMR 8028, F-75014 Paris, France

[2] Acad Sinica, Purple Mt Observ, Nanjing 210008, Peoples R China

[3] Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2008年 / 464卷 / 2093期

关键词：

n-body problem; central configuration; symmetry;

D O I：

10.1098/rspa.2007.0320

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We study the relationship between the masses and the geometric properties of central configurations. We prove that, in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

引用

页码：1355 / 1365

页数：11

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