講演・口頭発表等

2019年7月21日

Bifurcation of Simó H solution bifurcated from figure-eight choreographies of the equal mass three-body problem

天体力学N体力学研究会2019
  • Hiroshi Fukuda
  • ,
  • Toshiaki Fujiwara
  • ,
  • Hiroshi Ozaki

開催年月日
2019年7月20日 - 2019年7月21日
記述言語
英語
会議種別
ポスター発表
開催地
北里大学 相模原キャンパス L1号館 6階 61, 62 番教室, 相模原, [21日 12:00-14:00]
国名
日本

H solution found by Simó is a periodic orbit of equal mass three bodies which is very close to the famous figure-eight choreography but consists of three distinct orbits. By changing the power a of interaction potential $-1/r^a$ between bodies, the H solution coincides with the figure-eight choreography at a=0.9966. In this study, we calculate numerically the eigenvalue problem on the Hessian operator corresponding to the second variation of the action then investigate the bifurcation of the H solution. The eigenvalues and the eigenfunctions show that 1) the figure-eight choreography bifurcates from/to the H solution at a=0.9966 as above, 2) the H solution annihilates and bifurcates to the orbit with the same symmetry at a=0.816 and a=1.027. 3) Collision in the orbits seems to occur around a=0.9 and a=1.0. This is a joint work with Toshiaki Fujiwara and Hiroshi Ozaki.

リンク情報
共同研究・競争的資金等の研究課題
非斉次ポテンシャルで相互作用する3体問題周期解の数値計算による研究
URL
https://sites.google.com/site/instclassicalmech/shu-xue-jiao-yu-yan-jiu/2019-sagamihara