两对相邻等质量的四体共圆中心构型
Four-Body Co-Circular Central Configurations with Two Pairs of Adjacent Equal Masses
DOI: 10.12677/MP.2017.73006, PDF, HTML, XML, 下载: 1,520  浏览: 4,922  国家自然科学基金支持
作者: 马明俊*, 邓义杨：四川大学数学学院，四川 成都
关键词: 四体共圆问题；中心构型；等腰梯形；Four-Body Co-Circular Problem； Central Configurations； Isosceles Trapezoid
摘要: Cors和Roberts在2012年的文章[1]中证明了：在四体共圆中心构型中，若两对相邻质点的质量相等，则该共圆中心构型一定是等腰梯形。但是证明方法很复杂，本文采用有向面积方法并结合相对距离坐标给出了一个简洁证明。
Abstract: In 2012, Cors and Roberts [1] showed that the four-body co-circular central configuration is an isosceles trapezoid when two pairs of adjacent masses are equal. However, their proof is very complicated. In this paper, we give a simpler proof by using the method of oriented areas and mutual coordinates.
文章引用：马明俊, 邓义杨. 两对相邻等质量的四体共圆中心构型[J]. 现代物理, 2017, 7(3): 37-43. https://doi.org/10.12677/MP.2017.73006

参考文献

[1] Cors, M. and Roberts, E. (2012) Four-Body Co-Circular Central Configurations. Nonlinearity, 25, 343-370.
https://doi.org/10.1088/0951-7715/25/2/343
[2] Wintner, A. (1941) The Analytical Foundations of Celestial Mechanics. Princeton Math. Series 5. Princeton University Press, Princeton.
[3] Cayley, A. (1841) On a Theorem in the Geometry of Position. Cambridge Mathematical Journal, 2, 267-271.
[4] Dziobek, O. (1900) Über Einen Merkwürdigen Fall des Viclkörpronlems. Astronomische Nachrichten, 152, 32-46.
https://doi.org/10.1002/asna.19001520302
[5] Perez-Chavela, E. and Santoprete, M. (2007) Convex Four-Body Central Configurations with Some Equal Masses. Archive for Rational Mechanics and Analysis, 185, 481-494.
https://doi.org/10.1007/s00205-006-0047-z
[6] Deng, Y., Li, B. and Zhang, S. (2017) Four-Body Central Configurations with Adjacent Equal Masses. Journal of Geometry and Physics, 114, 329-335.
https://doi.org/10.1016/j.geomphys.2016.12.009