数学
最大值和最小值
正多边形
转动惯量
平面的
简单(哲学)
凸体
功能(生物学)
组合数学
订单(交换)
纯数学
凸函数
数学分析
几何学
凸优化
经典力学
物理
哲学
计算机图形学(图像)
认识论
财务
进化生物学
计算机科学
经济
生物
标识
DOI:10.1016/j.jde.2003.10.001
摘要
We give a simple proof of a classical result of MacMillan and Bartky (Trans. Amer. Math. Soc. 34 (1932) 838) which states that, for any four positive masses and any assigned order, there is a convex planar central configuration. Moreover, we show that the central configurations we find correspond to local minima of the potential function with fixed moment of inertia. This allows us to show that there are at least six local minimum central configurations for the planar four-body problem. We also show that for any assigned order of five masses, there is at least one convex spatial central configuration of local minimum type. Our method also applies to some other cases.
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