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A New Kind of Conjugate-nested Central Configurations in Consisted of One Regular Tetrahedron and One Regular Octahedron
  • ISSN号:1002-0462
  • 期刊名称:《数学季刊:英文版》
  • 时间:0
  • 分类:O175.7[理学—数学;理学—基础数学]
  • 作者机构:[1]College of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing 404000, China
  • 相关基金:Foundation item: Supported by NSF of China(10231010); Supported by NSF of Chongqing Education Committee(071105); Supported by NSF of SXXYYB(070X)
中文摘要:

在 R3 的一种新盒子配置,结合巢由一个常规四面体和一常规八面体组成了是配置是的 discussed.If 一种中央配置,当时,外面的层的所有群众是相等的,里面的群众层也是 equivalent.At 一样的时间在 p 之间的下列关系( r=3/3 是尺寸的半径比率)并且集体比率 r=m/m 一定是满足的r=-m/m=( +3 )( 3+2+2 )为任何妈的 -3/2+(-+3)(3-2+2)-3/2-4.2-3/2-2-4-1-2/2(1+)(3+2+2)-3/2+2(-1)(3-2+2)-3/2-4(22)-3,and

英文摘要:

A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ(r =√3/3ρ is the radius ratio of the sizes) and mass ratio τ=~↑m/m must be satisfied τ=~↑m/m=ρ(ρ+3)(3+2ρ+ρ^2)^-3/2+ρ(-ρ+3)(3-2ρ+ρ^2)^-3/2-4.2^-3/2ρ^-2-^-1ρ^-2/2(1+ρ)(3+2ρ+ρ^2)^-3/2+2(ρ-1)(3-2ρ+ρ^2)^-3/2-4(2√2)^-3ρ, and for any mass ratio τ, when mass ratio r is in the open interval (0, 0.03871633950 ... ), there exist three central configuration solutions(the initial configuration conditions who imply hamagraphic solutions) corresponding radius ratios are r1, r2, and r3, two of them in the interval (2.639300779… , +∞) and one is in the interval (0.7379549890…, 1.490942703… ). when mass ratio τ is in the open interval (130.8164950… , +∞), in the same way there have three corresponding radius ratios, two of them in the interval (0, 0.4211584789... ) and one is in the interval (0.7379549890…, 1.490942703…). When mass ratio τ is in the open interval (0.03871633950…, 130.8164950…), there has only one solution r in the interval (0.7379549890…, 1.490942703… ).

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期刊信息
  • 《数学季刊:英文版》
  • 北大核心期刊(2004版)
  • 主管单位:
  • 主办单位:河南大学
  • 主编:胡和生 林群
  • 地址:河南省开封市明伦街85号河南大学
  • 邮编:475001
  • 邮箱:
  • 电话:0378-3881698
  • 国际标准刊号:ISSN:1002-0462
  • 国内统一刊号:ISSN:41-1102/O1
  • 邮发代号:36-170
  • 获奖情况:
  • 1998年河南省优秀科技期刊二等奖. 2000年河南省优...
  • 国内外数据库收录:
  • 美国数学评论(网络版),德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊(2004版)
  • 被引量:468