平面(kN+1)体问题正多边形解的简明数值方法  

A CONCISE NUMERICAL ANALYSIS OF REGULAR POLYGON SOLUTIONS FOR(kN+1)-BODY PROBLEM

作　　者：刘文忠[1] 

机构地区：[1]北京师范大学天文学系,北京100875

出　　处：《北京师范大学学报（自然科学版）》2011年第2期134-137,共4页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10473002,10373004);科技部国家基础科学规划“973”资助项目(2009CB24901)

摘　　要：讨论平面kN或(kN+1)体问题正多边形解的数值方法.依照力学原理,建立正多边形解的条件方程组,把解微分方程组的问题,转化为解非线性方程组的问题.当质点的质量给定时,用牛顿迭代法解条件方程组.如果给定正多边形的外接圆半径,直接解线性的条件方程组就可以获得答案.A numerical solution for coplanar （κN＋1） body problem is provided. Constraint equations satisfying the coplanar N-body system is set up according to Newtonian dynamic principle. The problem of solving a set of differential equations is transformed into solving a nonlinear set of equations. With the mass of each object in the system given, solution to constraint equations can be obtained by Newtonian iteration. On the other hand, solution to the linear set of constraint equations is obtained if radius of circle enclosing each regular polygon is given.

关 键 词：(kN+1)体问题 正多边形解 数值方法 

分 类 号：O157[理学—数学]