论文标题
Pfaffians和共线中心配置的反问题
Pfaffians and the inverse problem for collinear central configurations
论文作者
论文摘要
我们考虑，在Albouy-Moeckel之后，共线中心配置的逆问题：给定$ N $身体的划线配置，找到使其中心的正质量。我们给出了有关Albouy-Moeckel Pfaffians的积极性的一些新估计：我们表明，对于任何同质性$α$和$ n \ leq 6 $或$ n \ leq 6 $或$ n \ leq 10 $和$α= 1 $（计算机辅助）Pfaffians是阳性的。此外，对于积极质量的逆问题，我们表明，对于任何同质性和$ n \ geq 4 $，配置空间的明确区域没有逆问题解决方案。
We consider, after Albouy-Moeckel, the inverse problem for collinear central configurations: given a collinear configuration of $n$ bodies, find positive masses which make it central. We give some new estimates concerning the positivity of Albouy-Moeckel pfaffians: we show that for any homogeneity $α$ and $n\leq 6$ or $n\leq 10$ and $α=1$ (computer-assisted) the pfaffians are positive. Moreover, for the inverse problem with positive masses, we show that for any homogeneity and $n\geq 4$ there are explicit regions of the configuration space without solutions of the inverse problem.
