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}

被引:0
作者
Małgorzata Moczurad
Piotr Zgliczyński
机构
[1] Jagiellonian University,Faculty of Mathematics and Computer Science
关键词
Central configurations; Symmetries; Interval arithmetic; Krawczyk operator;
D O I
10.1007/s10569-019-9920-6
中图分类号
学科分类号
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\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} with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For n=8,9,10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=8,9,10$$\end{document}, we establish the existence of central configurations without any reflectional symmetry.
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