2013 Fiscal Year Final Research Report
The figure-eight solution and Saari's conjecture in the-body problem
| Project/Area Number |
23540249
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kitasato University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 力学系 / 三体問題 / Saari予想 / 等質量 / 一般の質量 |
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| Research Abstract |
We proved the Saari's conjecture for the planar three-body problem under the Newton potential (the potential energy U is proportional to one over r, where r represents the mutual distance of bodies) and a strong force potential (U is proportional to one over r square). The Saari's conjecture is a conjecture in the N-body problem which claims that if a certain quantity "the configurational measure" is constant then the motion is homograpic. For the three-body problem, it claims that the motions with constant cofigurational measure are only the Euler's collinear solutions and the Lagrange's equilateral triangle solution.
We started our research to find a good variables to discribe the motion of the shape, then we succesfully proved the conjecture for equal masses case. The results are published. Recently, we finally proved the conjecture for general masses case. I will give a talk for this new result in a international conference in Jun 2014.
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