Families of three-dimensional periodic solutions in the circular restricted four-body problem

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• 作者：K. E. Papadakis
• 关键词：Four ; body problem ; Stability ; Three ; dimensional orbits ; Vertical ; critical orbits
• 刊名：Astrophysics and Space Science
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：361
• 期：4
• 全文大小：2,547 KB
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• 作者单位：K. E. Papadakis (1)
  
  1. Department of Civil Engineering, Division of Structural Engineering, University of Patras, 26504, Patras, Greece
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Astronomy
  
• 出版者：Springer Netherlands
• ISSN：1572-946X

文摘

In this paper we study the 3D symmetric periodic orbits of the circular restricted four-body problem, through their bifurcation from plane orbits. To this end, we calculate the special generating planar periodic orbits, i.e. the vertical-critical orbits, from five basic planar families of symmetric periodic orbits of the problem. We study the simplest 3D periodic orbits and so we restrict our calculations to simple vertical bifurcation orbits leading to families of one or two revolutions three-dimensional symmetric periodic orbits. We found 21 such families of simple 3D symmetric periodic orbits and typical orbits of all symmetry type 3D orbits are presented. The stability of each calculated 3D periodic orbit is also studied. Characteristic curves as well as stability diagrams of families of 3D periodic orbits are illustrated.