Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential
| Autor: | Fujiwara, Toshiaki, Fukuda, Hiroshi, Ozaki, Hiroshi, Taniguchi, Tetsuya |
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| Rok vydání: | 2015 |
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| Zdroj: | J. Phys. A: Math. Theor. 48, 265205 (2015) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/48/26/265205 |
| Popis: | Saari's homographic conjecture claims that, in the N-body problem under the homogeneous potential, $U=\alpha^{-1}\sum m_i m_j/r_{ij}^\alpha$ for $\alpha\ne 0$, a motion having constant configurational measure $\mu=I^{\alpha/2}U$ is homographic, where $I$ represents the moment of inertia defined by $I=\sum m_i m_j r_{ij}^2/\sum m_k$, $m_i$ the mass, and $r_{ij}$ the distance between particles. We prove this conjecture for general masses $m_k>0$ in the planar three-body problem under Newton potential ($\alpha=1$) and a strong force potential ($\alpha=2$). Comment: Submitted to Journal of Physics A |
| Databáze: | arXiv |
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