平面kN体问题正多边形解的简明数值方法  

A CONCISE NUMERICAL ANALYSIS ON REGULAR POLYGON SOLUTIONS FOR kN-BODY PROBLEM

作　　者：刘文中[1] 张同杰[1] 徐玢[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）》2005年第4期386-388,共3页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10473002;10373004);北京师范大学青年基金资助项目(1077002)

摘　　要：讨论平面kN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.The numerical method of solving the coplanar kN-body problem is studied. According to Newton＇s dynamic principle, the constraint equations that the coplanar N-body system satisfies are set up. Thus the problem of solving the set of differential equations is transformed into that of solving the nonlinear set of equations. Given the mass of each object in the system, the solution to the constraint equations is obtained by Newtonian iteration. On the other hand, the solution can be obtained by solving the linear set of constraint equations if the radius of the circle circumscribed to each regular polygon are given.

关 键 词：kN问题 正多边形解 数值方法 

分 类 号：O174.4[理学—数学]