Central configurations in planar n-body problem with equal masses for n=5, 6, 7

被引：0

作者：

Moczurad, Malgorzata ^{[1
]}

Zgliczynski, Piotr ^{[1
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Ul Prof Stanislawa Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 2019年 / 131卷 / 10期

关键词：

Central configurations; Symmetries; Interval arithmetic; Krawczyk operator; FINITENESS;

D O I：

10.1007/s10569-019-9920-6

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We give a computer-assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for n = 5, 6, 7 with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For n = 8, 9, 10, we establish the existence of central configurations without any reflectional symmetry.

引用

页数：28

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[2] Central configurations in planar n-body problem with equal masses for n=5,6,7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=5,6,7$$\end{document}
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