A regularization of the three-body problem
A regularization of the three-body problem
复制标题
三体问题的正则化
DOI：
10.1007/bf01227619
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发表时间：
1974
期刊：
影响因子：
--
通讯作者：
K. Zare
中科院分区：
文献类型：
--
作者：
S. Aarseth;K. Zare
设r_1，r_2，r_3为非零相互作用质点m_1，m_2，m_3的任意坐标，并定义距离R_1 =| r1−r3|，R2=| r2−r3|，R=| r1−r2|.本文给出了一般三体问题的一个八维正则化，它是基于单个双星的Kustaanheimo-Stiefel正则化，并具有以下性质：（i）对于两体碰撞R1 →0或R2 →0，运动方程是正则的。（ii）只要R <$R1或R <$R2，运动方程在近距离三重相遇时数值表现良好。
尽管要求R_（R1，R2）可能涉及到偶尔的物理变量变换，以重新标记粒子，但所有的积分都是在正则化变量中进行的。与标准的Kustaanheimo-Stiefel正则化的数值比较表明，新方法提供了改进的精度，每个积分步骤，在没有额外的计算时间的各种例子。此外，时间反演试验表明，临界三重相遇现在可以研究与confidence. Hamilton公式已推广到包括扰动三体运动的情况下，预计这一程序将导致进一步改善ofN体计算。
AbstractLetr1,r2,r3 be arbitrary coordinates of the non-zero interacting mass-pointsm1,m2,m3 and define the distancesR1=|r1−r3|,R2=|r2−r3|,R=|r1−r2|. An eight-dimensional regularization of the general three-body problem is given which is based on Kustaanheimo-Stiefel regularization of a single binary and possesses the properties:(i)The equations of motion are regular for the two-body collisionsR1→0 orR2→0.(ii)Provided thatR≳R1 orR≳R2, the equations of motion are numerically well behaved for close triple encounters.
Although the requirementR≳ min (R1,R2) may involve occasional transformations to physical variables in order to re-label the particles, all integrations are performed in regularized variables. Numerical comparisons with the standard Kustaanheimo-Stiefel regularization show that the new method gives improved accuracy per integration step at no extra computing time for a variety of examples. In addition, time reversal tests indicate that critical triple encounters may now be studied with confidence.The Hamiltonian formulation has been generalized to include the case of perturbed three-body motions and it is anticipated that this procedure will lead to further improvements ofN-body calculations.