The 1223 new periodic orbits of planar three-body problem with unequal
mass and zero angular momentum
X. Li, Y. Jing, and S. Liao. (2017)cite arxiv:1709.04775Comment: 84 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.00527.
Abstract
We present 1349 families of Newtonian periodic planar three-body orbits with
unequal mass and zero angular momentum and the initial conditions in case of
isosceles collinear configurations. These 1349 families of the periodic
collisionless orbits can be divided into seven classes according to their
geometric and algebraic symmetries. Among these 1349 families, 1223 families
are entirely new, to the best of our knowledge. Furthermore, some periodic
orbits have the same free group element for different mass. We find that the
scale-invariant average period linearly increases with the mass of one body
when the masses of the other two are constant. It is suggested that the masses
of bodies may play an important role in periodic three-body systems. The movies
of these periodic orbits are given on the website
http://numericaltank.sjtu.edu.cn/three-body/three-body-unequal-mass.htm .
Description
[1709.04775] The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum
%0 Generic
%1 li2017periodic
%A Li, Xiaoming
%A Jing, Yipeng
%A Liao, Shijun
%D 2017
%K 2017 mechanics paper physics
%T The 1223 new periodic orbits of planar three-body problem with unequal
mass and zero angular momentum
%U http://arxiv.org/abs/1709.04775
%X We present 1349 families of Newtonian periodic planar three-body orbits with
unequal mass and zero angular momentum and the initial conditions in case of
isosceles collinear configurations. These 1349 families of the periodic
collisionless orbits can be divided into seven classes according to their
geometric and algebraic symmetries. Among these 1349 families, 1223 families
are entirely new, to the best of our knowledge. Furthermore, some periodic
orbits have the same free group element for different mass. We find that the
scale-invariant average period linearly increases with the mass of one body
when the masses of the other two are constant. It is suggested that the masses
of bodies may play an important role in periodic three-body systems. The movies
of these periodic orbits are given on the website
http://numericaltank.sjtu.edu.cn/three-body/three-body-unequal-mass.htm .
@misc{li2017periodic,
abstract = {We present 1349 families of Newtonian periodic planar three-body orbits with
unequal mass and zero angular momentum and the initial conditions in case of
isosceles collinear configurations. These 1349 families of the periodic
collisionless orbits can be divided into seven classes according to their
geometric and algebraic symmetries. Among these 1349 families, 1223 families
are entirely new, to the best of our knowledge. Furthermore, some periodic
orbits have the same free group element for different mass. We find that the
scale-invariant average period linearly increases with the mass of one body
when the masses of the other two are constant. It is suggested that the masses
of bodies may play an important role in periodic three-body systems. The movies
of these periodic orbits are given on the website
\url{http://numericaltank.sjtu.edu.cn/three-body/three-body-unequal-mass.htm} .},
added-at = {2017-10-20T13:22:30.000+0200},
author = {Li, Xiaoming and Jing, Yipeng and Liao, Shijun},
biburl = {https://www.bibsonomy.org/bibtex/2e9ba3065a63c964200e4481c2893f166/achakraborty},
description = {[1709.04775] The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum},
interhash = {40b36c304b995d41db868273c70080c6},
intrahash = {e9ba3065a63c964200e4481c2893f166},
keywords = {2017 mechanics paper physics},
note = {cite arxiv:1709.04775Comment: 84 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.00527},
timestamp = {2017-10-20T13:22:30.000+0200},
title = {The 1223 new periodic orbits of planar three-body problem with unequal
mass and zero angular momentum},
url = {http://arxiv.org/abs/1709.04775},
year = 2017
}