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平面kN体问题正多边形解的简明数值方法 被引量：2

A CONCISE NUMERICAL ANALYSIS ON REGULAR POLYGON SOLUTIONS FOR kN-BODY PROBLEM
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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.
作者 刘文中 张同杰 徐玢
机构地区 北京师范大学天文学系
出处 《北京师范大学学报（自然科学版）》 CAS CSCD 北大核心 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)
关键词 kN问题 正多边形解 数值方法 kN-body problem regular polygon solution numerical method
分类号 O174.4 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Bruschi M, Calogero F. Solvable and /or integrable and/or linearizable N-body problems in ordinary (Three-Dimensional) space I[J]. Journal of Nonlinear Mathematical Physics, 2000, 7(3):303.
  • 2Perko L M , Walter E L. Regular polygon solutions of the N-body problem[J]. Proc AMS, 1985, 94:301.
  • 3Xie Z F, Zhang S Q. A simpler proof of regular polygon solutions of the N-body problem[J]. Phys Lett A, 2000, 277:156.
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同被引文献26

  • 1Bruschi M, Calogero F. Solvable and/or integrable and/or linearizable N-body problemsin ordinary (three-dimensional) space I [J]. Journal of Nonlinear Mathematical Physics, 2000, 7(3):303
  • 2Molina R, Vigueras A. The planar n-body problem:regular polygon solutions[J]. Applied Mathematics and Computation, 2004, 156:321
  • 3de Castro A S, Vilela C A. On the regular-geometricfigure solutions to the n-body problems[J]. Eur J Phys,2001, 22:478
  • 4Zhang Shiqing, Xie Zhifu. Nested regular polygon solutions of the 2n-body problem[J]. Physics Letters A,2001, 281.119
  • 5Perko L M. and Walter E L. Regular polygon solutions of the N-body problem[J]. Proc AMS, 1985, 94:301
  • 6Xie Zhifu, Zhang Shiqing. A simpler proof of regular polygon solutions of the N-body problem [J]. Physics Letters A, 2000, 277-156
  • 7Bruschi M, Calogero F. Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space I[J].Journal of Nonlinear Mathematical Physics, 2000, 7 (3) : 303
  • 8Meyer K R, Schmidt D S. Elliptic relative equilibria in the N-body problem[J]. Journal of Differential Equations(Article in Press)
  • 9Xia Zhihong. Convex central configurations for the N-body problem [J]. Journal of Differential Equations,2004, 200:185
  • 10Ouyang Tiancheng, Xie Zhifu, Zhang Shiqing. Pyramidal central configurations and perverse solutions [J].Electronic Journal of Differential Equations, 2004, 106 : 1

引证文献2

二级引证文献4

北京师范大学学报（自然科学版）
2005年 第4期

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