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A New Critical Value Concerning the Genealogy of Long Period Families at L_4 in the Restricted Three-body Problem

A New Critical Value Concerning the Genealogy of Long Period Families at L_4 in the Restricted Three-body Problem
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摘要 We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details. We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.
出处 《Chinese Journal of Astronomy and Astrophysics》 CSCD 2008年第1期103-107,共5页 中国天文和天体物理学报(英文版)
基金 Supported by the National Natural Science Foundation of China
关键词 celestial mechanics - restricted three-body problem- equilateral equilibrium point - periodic orbits celestial mechanics - restricted three-body problem- equilateral equilibrium point - periodic orbits
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参考文献6

  • 1Arnold V. I., 1999, Mathematical Methods of Classical Mechanics, Second Edition, Beijing: Springer-Verlag.
  • 2Deprit A., Henrard J., 1968, In: Z. Kopal, ed., Advances in Astronomy and Astrophysics, 6, Academic Press, p. 1.
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