Three-body figure-eight choreography under the universal gravitation in two dimensions

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400408
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Tokai University
• Principal Investigator: Ozaki Hiroshi 東海大学, 清水教養教育センター, 教授 (00407991)
• Co-Investigator(Kenkyū-buntansha): MATSUDA Katsumi 東海大学, 清水教養教育センター, 准教授 (10297195)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 3体問題 / 等質量3体8の字解 / 拡張された3接線定理 / 解析解 / 数値解析

Outline of Final Research Achievements

(1) We got a set of initial positions and velocities of equal mass three bodies in very high precision (over 10 significant figures)　such that equal mass three bodies under their mutual attractions in two dimensions chase each other in an figure-eight orbit.
(2) We found that the equal mass three-body choreographic solution in an arbitrary gravitational force field, to keep the center of mass being at the origin with zero total angular momentum, is constructed by two periodic functions. We also found that the equal mass three-body figure-eight choreographic solution is constructed by two even functions: one changes its sign as t → t+ω/2 and the other has a period of ω/6.

Free Research Field

数物系科学