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

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.