日時：2026/10/13(火) 15:00-16:00
場所：総合研究10号館317室
講演者：黒川大雅
タイトル：変分法による直線型配置に対する平面円制限(N+1)体問題の対称周期軌道の存在証明
アブストラクト：N体問題は3体以上で一般解が解析的に解けないことが知られている古典的かつ重要な課題である. 本研究では, 直線型中心配置に対する平面円制限(N+1)体問題（およびその一般化）を対象とし, その直線に対称な周期解の存在証明を行う. 先行研究では, N=2に対し変分法を用いた周期解の存在証明がなされている一方（Kajihara & Shibayama, 2022）, N≧3に対する変分法を用いた統一的な研究は行われていなかった. 本研究では, この方法を一般のN体直線配置に拡張し, その直線に対称な周期解が存在するための十分条件を証明した. 本講演では, 主結果のほか, 変分法による対称周期解の構成法やN体問題における変分法の難しさの概略を紹介し, 他分野との活発な議論を目指す.
Date: From 3 p.m. to 4 p.m. Tuesday, October 13th, 2026
Location: Room 317, Research Bldg. No. 10
Speaker: Taiga Kurokawa
Title: Existence of Symmetric Periodic Orbits in the Planar Circular Restricted (N+1)-Body Problem for Collinear Configurations via Variational Methods
Abstract: The N-body problem is a classical and fundamental problem, well known for having no general analytical solutions for three or more bodies. In this study, we focus on the planar circular restricted (N+1)-body problem for collinear central configurations (as well as its generalizations) and prove the existence of periodic solutions symmetric with respect to the line of bodies. While previous work established the existence of such periodic solutions for N=2 using variational methods (Kajihara & Shibayama, 2022), no unified variational approach had been carried out for N≧3. We extend this method to general N-body collinear configurations and prove a sufficient condition for the existence of line-symmetric periodic solutions. In this presentation, in addition to the main results, we will outline the construction of symmetric periodic solutions via variational methods and explain the technical difficulties encountered when applying variational approaches to the N-body problem, with the aim of encouraging active discussion across related fields.