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2N体问题两层正多边形中心构型 被引量：2

TWO LAYER REGULAR POLYGON CENTRAL CONFIGURATIONS OF 2N-BODY PROBLEMS
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摘要 研究2N体问题2层正多边形中心构型.给出了2层正多边形中心构型存在的条件方程,论证了解的存在性. Two layer regular polygon central configurations of 2N-body problems are studied. The conditional equations and existence proof of these solutions of the problems are given.
作者 刘文忠 马利华 尹志强
机构地区 北京师范大学天文学系 中国科学院国家天文台
出处 《北京师范大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第6期624-626,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)
关键词 2N体问题 两层正多边形 中心构型 2N-body problem two layer regular polygon central configurations
分类号 P132 [天文地球—天体力学]
  • 相关文献

参考文献26

  • 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.
  • 2Simo C. New families of solutions in N-body problem [C ] // Proceedings of European Congress of Mathematicians. Boston: Birkhauser, 2000.
  • 3Meyer K R, Schmidt D S. Elliptic relative equilibria in the N-body problem[J]. Journal of Differential Equations, Article in press.
  • 4Xia Zhihong. Convex central configurations for the Nbody problem[J]. Journal of Differential Equations, 2004, 200:185.
  • 5Ouyang Tiancheng, Xie Zhifu, Zhang Shiqing. Pyramidal central configurations and perverse solutions[J]. Electronic Journal of Differential Equations, 2004, 106.1.
  • 6刘学飞.一类以凹五边形为基底的7-体双金字塔中心构型[J].西南师范大学学报（自然科学版）,2002,27(4):494-496. 被引量：3
  • 7Liu Xuefei. Double pyramidal central configurations with a concave quadrilateral base[J]. Journal of Chongqing University:Eng ed. 2002, 1(1):67.
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  • 9XieZhifu ChenQi''an.Pyramidal central configurations for spatial 5-body problems.重庆大学学报：自然科学版,2001,24(1):122-122.
  • 10Liu Xuefei. Double pyramidal central configurations with a concave quadrilateral base[J]. Journal of Chongqing University: Eng. ed. 2002, 1(1)167.

二级参考文献23

  • 1[1]Perko L M, Walter E L. Regular polygon solutions of the N-body problem. Proc AMS, 1985, 94:301～309
  • 2[2]Moeckel R, Simo C. Bifurcation of spatial central configurations from planar ones. SIAM J Math Anal, 1995,26:978～998
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  • 4[4]Elmabsout B. Sur L'existence des certaines configurations d'equilibre relatif dans le probleme des N corps.Mech, 1988, 41:131～151
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  • 8[2]Meyer K, Hall G. Introduction to Hamiltonian Systems and the N-body Problems, Berlin: Springer-Verlag,1992
  • 9[3]Moeckel R, Simo C. Bifurcation of spatial central configurations from planar ones. SIAM J Math Anal, 1995,26:978～998
  • 10[4]Wintner A. Analytical Foundations of Celestial Mechanics. Princeton: Princeton Univ Press, 1941

共引文献14

同被引文献47

  • 1刘文中,孙艳春,尹志强,刘梦.N体问题的正多面体解[J].北京师范大学学报（自然科学版）,2006,42(3):265-267. 被引量：3
  • 2刘文中,马利华,徐玢,张同杰.N体问题平面正多边形解[J].北京师范大学学报（自然科学版）,2006,42(5):486-488. 被引量：1
  • 3Herbert Goldsteiru Classical Mechanics[M]. 3rd ed.北京:高等教育出版社,2005:70.
  • 4Brusehi 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.
  • 5Xia Z, Convex central configurations for the N-body problem[J]. J Differential Equations, 2004,200:185.
  • 6Moeckel R, Simo C. Bifurcation of spatial central configurations from planar ones[J].SIAM J Math Anal, 1995,26 (4) : 978.
  • 7Zhang S. Two layer nested regular polygon central configurations in Ra[J]. Phys Lett A, 2001,290 : 49.
  • 8Meyer K R, Schmidt D S. Elliptic relative equilibria in the N-body problem[J]. J of Differential Equations, Article in press.
  • 9Ouyang T, Xie Z, Zhang X. Pyramidal central configurations and perverse solutions [J]. Electronic Journal of Differential Equations, 2004,106 : 1.
  • 10Saari D. On the role and properties of n body central configurations[J]. Celestial Mech, 1980,21:9.

引证文献2

二级引证文献1

北京师范大学学报（自然科学版）
2007年 第6期

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