论文标题
在等边五边形中央配置上
On the equilateral pentagonal central configurations
论文作者
论文摘要
等边五角大楼是平面中的多边形，其长度相等。在本文中，我们对$ 5 $ - 体问题的中心配置进行了分类，使五个尸体在等边五角大楼的顶点具有对称轴。我们证明，有两种独特的等值五角形提供了中央配置，一种凹形等边五角大楼和一个凸等于五角大楼，是常规的。我们证明的一个关键点是使用有理参数化将涉及正方根的相应方程转换为多项式方程。
An equilateral pentagon is a polygon in the plane with five sides of equal length. In this paper we classify the central configurations of the $5$-body problem having the five bodies at the vertices of an equilateral pentagon with an axis of symmetry. We prove that there are two unique classes of such equilateral pentagons providing central configurations, one concave equilateral pentagon and one convex equilateral pentagon, the regular one. A key point of our proof is the use of rational parameterizations to transform the corresponding equations, which involve square roots, into polynomial equations.
