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Science China Physics, Mechanics & Astronomy

, Volume 57, Issue 11, pp 2121–2126 | Cite as

On the stability of the three classes of Newtonian three-body planar periodic orbits

  • XiaoMing Li
  • ShiJun Liao
Article

Abstract

Currently, the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Šuvakov and Dmitra šinović [Phys Rev Lett, 2013, 110: 114301] using the gradient descent method with double precision. In this paper, these reported orbits are checked stringently by means of a reliable numerical approach (namely the “Clean Numerical Simulation”, CNS), which is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision with a procedure of solution verification. It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time, and are thus most possibly unstable at least. It is suggested to carefully check whether or not these seven unstable orbits are the so-called “computational periodicity” mentioned by Lorenz in 2006. This work also illustrates the validity and great potential of the CNS for chaotic dynamic systems.

Keywords

three body problem periodic orbit stability computational reliability Clean Numerical Simulation (CNS) 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Ministry-of-Education Key Laboratory in Scientific ComputingShanghaiChina
  2. 2.School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghaiChina
  3. 3.Nonlinear Analysis and Applied Mathematics Research Group (NAAM)King Abdulaziz University (KAU)JeddahSaudi Arabia

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