Variational approach to the n-body problem
Project/Area Number |
22740104
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Global analysis
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Research Institution | Osaka University (2011-2013) Kyoto University (2010) |
Principal Investigator |
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Project Period (FY) |
2010-04-01 – 2014-03-31
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Project Status |
Completed (Fiscal Year 2013)
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Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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Keywords | 多体問題 / 変分法 / 周期解 / 天体力学 / 力学系 / カオス / 分岐 / 対称性 / 特異点 / スケーリング / ブローアップ / N体問題 / ハミルトン力学系 / 衝突 / 摂動論 / 勾配法 / 峠の定理 / 特異点解析 / 可積分性 |
Research Abstract |
I proved the existence of periodic solutions with regularizable collisions in the n-body problem. This includes the proof of the existence of Schubart orbit with arbitrary masses in the collinear three-body problem, Broucke orbit in the isosceles three-body problem and Sekiguchi orbit in the symmetric collinear four-body problem. I also proved the existence of super-eight solution by using the variational method.We investigated the bifurcation phenomena on periodic solutions in the isosceles three-body problem. I proved the non-integrability of the collinear three-body problem by using the collision manifold theory.
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Report
(5 results)
Research Products
(47 results)
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[Presentation] 天体の周期運動2012
Author(s)
柴山允瑠
Organizer
研究会「非線形現象の解明と制御」
Place of Presentation
大阪大学基礎工学研究科
Year and Date
2012-10-04
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