2016/06/30 by Hiroshi Fukuda, Toshiaki Fujiwara, Hiroshi Ozaki · 1 citation
Mathematics · Physics and Astronomy · #math.DS #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/aa5741
published as J. Phys. A: Math. Theor. 50 105202 (2017) · This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/aa5741
arxiv created 2017/01/06 · arxiv updated 2019/01/07
We report on figure-eight choreographic solutions to a system of three identical particles interacting through a potential of Lennard-Jones type, 1/r12-1/r6 where r is a distance between the particles. By numerical search, we found there are a multitude of such solutions. A series of them are close to a figure-eight solutions to a homogeneous system with no 1/r12 term in the potential. The rest are very different from them and have several points with large curvatures in their figure-eight orbits, at which particles are repelled. Here figure-eight choreographies are the periodic motion whose shape is symmetric in both horizontal and vertical axis, starting with an isosceles triangle configuration and going back to an isosceles triangle configuration with opposite direction through Euler configuration. Thus the lobe of this figure-eight may be complex shape and needs not to be convex.