Planarity conditions and four-body central configurations equations with angles as coordinates

被引：1
作者：
Santoprete, Manuele [1 ]
机构：
[1] Wilfrid Laurier Univ, Dept Math, Waterloo, ON, Canada
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2019年 / 140卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
n-body problem; Central configurations; Celestial mechanics; SYMMETRY;
D O I：
10.1016/j.geomphys.2018.09.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss several conditions for four points to lie on a plane, and we use them to find new equations for four-body central configurations that use angles as variables. We use these equations to give novel proofs of some results for four-body central configuration. We also give a clear geometrical explanation of why Ptolemy's theorem can be used to write equations for co-circular central configurations when mutual distances are used as coordinates. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：74 / 84
页数：11
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