On the Lagrange and Hill stability of motion in the three-body problem

In the three-body problem, we consider the Lagrange and Hill stability including the Lagrange stability for the manifold of symmetric motions that exists in the case where two of three bodies have equal masses. To analyze the stability, in addition to integrals of energy and angular momentum we use the Lagrange–Jacobi equality. We prove theorems on the Lagrange and Hill stability. The theorem on the Hill stability has effective application in the case where the mass of a body is much less than masses of two other bodies. In this case, as it is known, the model of the restricted three-body problem is usually applied.     

β-分布的渐近抽样法及其在计算机上的实现

迄今,在一般的随机模拟文献中,关于β分布的抽样主要讨论参数为正整数情形。本文借助于Polya罐子模型黑球比例数X_的极限分布为β—分布这一原理,提出了正有理参数β—分布的渐近抽样方法,给出了模拟算法,编制了程序。选取若干正有理数参数,在计算机上进行了随机模拟,产生了渐近于β—分布的随机数,并制成了随机数表。本文对其中一些样本应用各种统计方法进行了检验,结果表明,拟合性是非常好的。