For total collision solutions of the \(n\)-body problem, Chazy showed that the overall size of the configuration converges to zero with asymptotic rate proportional to \(|T-t|^{\frac{2}{3}}\) where \(T\) is the collision time. He also showed that the shape of the configuration converges to the set of central configurations. If the limiting central configuration is nondegenerate, the rate of convergence of the shape is of order \(O(|T-t|^{p})\) for some \(p>0\). Here we show by example that in the planar four-body problem there exist total collision solutions whose shape converges to a degenerate central configuration at a rate which is slower that any power of \(|T-t|\).

对于\(n\)体问题的总碰撞解，Chazy 表明配置的整体大小收敛到零，渐进率与\(|Tt|^{\frac{2}{3}}\)成正比其中\(T\)是碰撞时间。他还表明，构型的形状收敛于中心构型集。如果限制中心配置是非简并的，则对于某些\(p>0\) ，形状的收敛速度为\(O(|Tt|^{p})\)。这里我们通过例子证明，在平面四体问题中，存在总碰撞解，其形状收敛到简并中心构型的速度比 \(|Tt|\) 的任何幂都要慢。