On the stability of the three classes of Newtonian three-body planar periodic orbits
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.
- Publication:
-
Science China Physics, Mechanics, and Astronomy
- Pub Date:
- November 2014
- DOI:
- arXiv:
- arXiv:1312.6796
- Bibcode:
- 2014SCPMA..57.2121L
- Keywords:
-
- three body problem;
- periodic orbit;
- stability;
- computational reliability;
- Clean Numerical Simulation (CNS);
- Astrophysics - Earth and Planetary Astrophysics
- E-Print:
- 5 pages, 5 figures