一类具非零角动量的平面三体系统的数值分析

Numerical Analysis of a Class of Planar Three-Body Systems with Nonzero Angular Momenta

对一类具非零角动量的平面三体系统研究其三体构形对系统演化的影响。根据Agekian和Anosova提出的构形图(homology map),三体系统按其构形特点分属于4个不同的区域。通过数值计算,考察了初始位置位于不同区域中的构形颗粒(homologydrop)的演化,并就有关性质与Heinamaki等人研究的角动量为零的三体系统作了比较指出,构形颗粒的组成系统全部发生解体的时间在L区域最早,H区域最晚,这与零角动量系统不同。还对4个区域的三体系统的寿命进行了统计分析,得到了各区域中未解体的系统数随时间指数衰减的函数关系。

A class of the planar three-body systems with nonzero angular momenta is studied. The main aim is to find out the effects of this system's initial configuration on its dynamical evolution. According to the homology map first suggested by Agekian & Anosova, a planar three-body systems corresponds to a point of one of 4 characteristic regions. By comparing the evolutions of the homology drops in the nonzero-angular-momentum three-body systems with the zero-angular-momentum systems (P.Heinamaki et al, 1999), we found the similarity of the mixing extent of the homology drops in the homology map, and the difference in the functions of the number of surviving systems versus time in those drops. And through the statistics of the evolution time of the systems, we obtain the following results: (i) the mean lifetimes of the systems of the 4 regions are different; (ii) there is an exponential relationship between the number N of the surviving systems and the evolution time t.