3n体三重嵌套正多边形中心构型问题

Central configurations for planar 3n-body problem: triple nested regular polygons

作者：邓春华(淮阴工学院数理学院)；苏霞(淮阴工学院数理学院)

Author：DENG Chun-Hua(Faculty of Mathematics and Physics, Huaiyin Institute of Technology)；SU Xia(Faculty of Mathematics and Physics, Huaiyin Institute of Technology)

收稿日期：2018-03-08 年卷（期）页码：2018,55(5):917-928

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：多体问题；平面中心构型；嵌套正多边形；牛顿势.

Key words：n-body problem; Planar central configuration; Nested regular polygon; Newtonian law

基金项目：国家自然科学基金青年基金(11703006)；淮阴工学院科研基金（15HGZ014, 17HGZ004）

中文摘要

本文运用Dziobek方程组研究了9体和12体三重嵌套正多边形中心构型问题. 对于9体问题, 本文发现了三类新的三重嵌套正三角形中心构型. 对于12体问题,本文也发现了几类不同的三重嵌套正多边形中心构型.

英文摘要

We study the existence of some families of triple nested planar central configurations for the n-body problem with n=9, 12. For 9-body problem we show that there exist three families of triple nested triangular central configurations. For 12-body problem we show that there exist different families of triple nested regular polygonal central configurations in different cases.

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论文摘要

3n体三重嵌套正多边形中心构型问题

Central configurations for planar 3n-body problem: triple nested regular polygons