A stochastic optimization algorithm for analyzing planar central and balanced configurations in the n-body problem

被引：0
作者：
Alexandru Doicu
Lei Zhao
Adrian Doicu
机构：
[1] Universität Ausgburg,Institut für Mathematik
[2] Deutsches Zentrum für Luft- und Raumfahrt (DLR),Institut für Methodik der Fernerkundung (IMF)
来源：
Celestial Mechanics and Dynamical Astronomy | 2022年 / 134卷
关键词：
Central configuration; Balanced configuration; Stochastic optimization; Morse equality; Krawczyk operator;
D O I：
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学科分类号：
摘要：
A stochastic optimization algorithm for analyzing planar central and balanced configurations in the n-body problem is presented. We find a comprehensive list of equal mass central configurations satisfying the Morse equality up to n=12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=12$$\end{document}. We show some exemplary balanced configurations in the case n=5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=5$$\end{document}, as well as some balanced configurations without any axis of symmetry in the cases n=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=4$$\end{document} and n=10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=10$$\end{document}.
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