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arXiv · 1503.00407

Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential

Toshiaki Fujiwara·Hiroshi Fukuda·Hiroshi Ozaki·Tetsuya Taniguchi
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Abstract

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 ($\alpha=2$).

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Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki, Tetsuya Taniguchi. 2015-03-02. Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential. https://doi.org/10.1088/1751-8113/48/26/265205

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