论文标题
椭圆形限制的三体问题的kustaanheimo-stiefel正规化以及与快速Lyapunov指标的近距离相遇
A Kustaanheimo-Stiefel regularization of the elliptic restricted three-body problem and the detection of close encounters with fast Lyapunov indicators
论文作者
论文摘要
我们介绍了椭圆形限制的三体问题（ER3BP）的Kustaanheimo-Stiefel（KS）正规化，并讨论了其用于研究通过其山坡（快速接近接触者）的过渡类别的用途。从哈密顿式旋转式参考框架的哈密顿表示问题的表示开始，以及$ p_2 $作为自变量的真实异常，我们通过应用经典的KS变换和在次要的情况下执行类似于循环的情况下的正则化，并应用了循环的ks变换，以及在扩展的10二维相位空间中的等值量减少。使用这样的正规化汉密尔顿人，我们恢复了ER3BP中快速近距离相遇的定义，即质量参数$μ$的少量值（虽然我们不需要针对初选的偏心率的较小条件），并且我们表明，对于这些遇到的杂种方程的解决方案是通过在山上快速交易中的实用型增长来表征的。因此，对于小$μ$，我们证明了正规化快速lyapunov指标（RFLIS）的有效性，以检测具有多个快速近距离接触的轨道。最后，我们提供数值演示，并从计算成本方面显示正规化的好处。
We present the Kustaanheimo-Stiefel (KS) regularization of the elliptic restricted three-body problem (ER3BP) at the secondary body $P_2$, and discuss its use to study a category of transits through its Hill's sphere (fast close encounters). Starting from the Hamiltonian representation of the problem using the synodic rotating-pulsating reference frame and the true anomaly of $P_2$ as independent variable, we perform the regularization at the secondary body analogous to the circular case by applying the classical KS transformation and the iso-energetic reduction in an extended 10-dimensional phase-space. Using such regularized Hamiltonian we recover a definition of fast close encounters in the ER3BP for small values of the mass parameter $μ$ (while we do not require a smallness condition on the eccentricity of the primaries), and we show that for these encounters the solutions of the variational equations are characterized by an exponential growth during the fast transits through the Hill's sphere. Thus, for small $μ$, we justify the effectiveness of the regularized fast Lyapunov indicators (RFLIs) to detect orbits with multiple fast close encounters. Finally, we provide numerical demonstrations and show the benefits of the regularization in terms of the computational cost.
