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arXiv · 1107.2178

Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential

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

Donald Saari conjectured that the $N$-body motion with constant configurational measure is a motion with fixed shape. Here, the configurational measure $\mu$ is a scale invariant product of the moment of inertia $I=\sum_k m_k |q_k|^2$ and the potential function $U=\sum_{i 0$. Namely, $\mu = I^{\alpha/2}U$. We will show that this conjecture is true for planar equal-mass three-body problem under the strong force potential $\sum_{i<j} 1/|q_i-q_j|^2$.

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Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki, Tetsuya Taniguchi. 2011-07-12. Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential. https://doi.org/10.1088/1751-8113/45/4/045208

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