一类以凹五边形为基底的7-体双金字塔中心构型  

A Class of Double Pyramidal Central Configurations of 7-Body with Concave Pentagon Base

作　　者：刘学飞[1,2] 

机构地区：[1]重庆三峡学院数学系 [2]重庆大学数理学院应用数学系,重庆400044

出　　处：《西南师范大学学报（自然科学版）》2002年第4期494-496,共3页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目 (198710 96)

摘　　要：讨论了一类以凹五边形为基底的 7 体构成双金字塔中心构型的必要条件 .在某些对称条件下 ,给出了 7 体构成双金字塔中心构型的必要条件或充要条件 .如果m1,m2 ,… ,m7构成双金字塔中心构型 (其中m5位于m1,… ,m4构成的凸四边形的对角线的交点处 ,m6,m7的连线过m5且垂直于m1,m2 ,… ,m5构成的基底并且到基底的距离相等 ) ,那么 ,m6=m7;在该双金字塔中心构型中 ,若m1,… ,m4构成一伞形 ,则其中一条对角线上的两个质量相等 ;在该双金字塔中心构型中 ,m1,… ,m4构成平行四边形的充分必要条件是该平行四边形是菱形且每条对角线上的两个质量相等 ,m1,… ,m4构成矩形当且仅当该矩形为正方形且m1,… 。Some necessary conditions of a class of 7 body DPCC (double pyramidal central configuration) with concave pentagon base are proved, and some necessary and sufficient conditions of 7 body DPCC for some particularly symmetric assumptions are obtained. The following conclusions are obtained. If m 1, m 2, ..., m 7 form a DPCC with the concave pentagon base containing m 1, m 2, ..., m 5, and m 5 lies at the point of the intersection of the two diagonals of convex quadrilateral formed by m 1, m 2, ..., m 4. m 6, m 7 are at the end point of vertical line of the base plane and the vertical line passes m 5 , at the same times the distances that m 6, m 7 being from the base are equal, then m 6=m 7. If m 1, m 2, ..., m 4 of the DPCC form a kit shaped, then the masses at the two vertices of some diagonal of the kit shaped are equal. m 1, m 2, ..., m 4 of the DPCC form a parallelogram if and only if the parallelogram is a diamond, m 6=m 7 and two masses ofeach diagonal of the parallelogram are equal; and m 1, m 2, ..., m 4 of the DPCC form a rectangular if and only if the rectangular is a square and all masses m 1, m 2, ..., m 4 of the square are equal.

关 键 词：7-体 双金字塔中心构型 N-体问题 凹五边形基底 充分必要条件 位置向量 几何中心 

分 类 号：P132.4[天文地球—天体力学]