对数势条件下双层正方形中心构型的扭转角问题  

The Twisted Angle Problem of the Central Configuration of a Double Square with Logarithmic Potential

作　　者：曾小华 赵甫荣 李树勇 ZENG Xiaohua;ZHAO Furong;LI Shuyong(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan;College of Mathematical Physics,Mianyang Teacher’s College,Mianyang 621000,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]绵阳师范学院数理学院,四川绵阳621000

出　　处：《四川师范大学学报（自然科学版）》2023年第1期52-57,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11571245)。

摘　　要：研究一类中心构型存在的必要条件.针对由 z -轴垂直通过其中心的双层正方形构型,通过分析法,得到在对数势条件下,如果位于同一个正方形顶点的天体质量相等,则这2个正方形构成中心构型的必要条件是它们的扭转角等于 kπ/ 2 或者 ( π/ 4 + kπ/ 2 ).This paper is devoted to the necessary condition for the existence of a central configuration. For the configuration with two squares where the vertical z -axis passes through their center, by using analytical methods, it is found that the necessary condition of the two squares to form a central configuration is that its twisted angel is kπ/ 2 or ( π/ 4 + kπ/ 2 ) under the log-potential condition if the bodies at the vertices of the same square have equal masses.

关 键 词：对数势 正方形 中心构型 

分 类 号：O175.1[理学—数学]