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Melnikov方法和圆型平面限制性三体问题的横截同宿研究*

朱如曾 向程

朱如曾, 向程. Melnikov方法和圆型平面限制性三体问题的横截同宿研究*[J]. 应用数学和力学, 1996, 17(12): 1113-1122.
引用本文: 朱如曾, 向程. Melnikov方法和圆型平面限制性三体问题的横截同宿研究*[J]. 应用数学和力学, 1996, 17(12): 1113-1122.
Zhu Ruzeng, Xiang Cheng. Studies of Melnikov Method and Transversal Homoclinic Orbits in the Circular Planar Restricted Three-Body Problem[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1113-1122.
Citation: Zhu Ruzeng, Xiang Cheng. Studies of Melnikov Method and Transversal Homoclinic Orbits in the Circular Planar Restricted Three-Body Problem[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1113-1122.

Melnikov方法和圆型平面限制性三体问题的横截同宿研究*

基金项目: * 国家自然科学基金资助项目

Studies of Melnikov Method and Transversal Homoclinic Orbits in the Circular Planar Restricted Three-Body Problem

  • 摘要: 本文对由两自由度近可积哈密顿系统经非正则变换而得到的,具有高阶不动点的非哈密顿系统给出了判别横截同宿轨和横截异宿轨存在性的两条判据。对原二体质量比很小时近可积圆型平面限制性三体问题,采用本文判据证明存在横截同宿轨,从而存在横截同宿穿插现象;还在一定假设下证明了存在横截异宿轨;并给出了全局定性相图。
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    [6] R.Easton,Capture orbits and Melnikov integrals in the planar three-body problem,Cele.Mech.and Dyn.Astro.,50(1991),283-297.
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    [9] S.Wiggins,Global Bifurcations and Chaos,Springer-Verlag(1988).
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出版历程
  • 收稿日期:  1995-07-23
  • 修回日期:  1996-04-01
  • 刊出日期:  1996-12-15

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