Orbital Integration for Gravitational Three-body Problem based onTotally Conservative Integrator

三体问题是预测相互引力相互作用的三个质量的运动的问题。这个问题具有以下性质：(I)它守恒了确定其轨道所必需的一些量；(Ii)它具有时间可逆性。也就是说，它的反向时间演化的形式与向前时间演化的形式一致；(Iii)在某些初始条件下，它产生了平衡轨道。直到我们提出了一个保留所有(I)、(Ii)和(Iii)的轨道积分方案之前，一些只保留(I)和(Ii)的方案是已知的。在很长的时间间隔内，该格式精确地再现了其他通用积分器无法精确计算的各种周期轨道。

Three-body problem is the problem of predicting the motion of three masses that interact with each other gravitationally. This problem has the following properties: (i) it conserves some quantities which are necessary to determine its orbits; (ii)it has time reversibility. Namely, the form of its backward-time evolution coincides with that of forward-time evolution; (iii) it yields equilibrium orbits for some initial conditions. Until we proposed an orbital integration scheme which keeps all of (i), (ii) and (iii), some schemes retaining only (i) and (ii) were known. For a long time interval, the proposed scheme precisely reproduces various periodic orbits that cannot be accurately computed byother generic integrators.