标题： 平面三体问题快速近距离相遇的参数逼近作为焦点-焦点动力学的弧段 显示英文标题

标题： Parametric approximations of fast close encounters of the planar three-body problem as arcs of a focus-focus dynamics

摘要： 一个小型天体与行星的引力近距离相遇可能会显著改变其轨道参数，这些参数可以通过圆型限制三体问题进行研究。 在本文中，我们提供了平面CRTBP中与次级天体快速近距离相遇的参数表示，这些表示为非线性焦点-焦点动力学的弧线。 结果是该问题哈密顿量的伯克霍夫正规形式通过利维-奇维塔正则化表示时的一个显著分解的结果。 这些参数化是通过两个不同的给定阶数N的伯克霍夫正规化序列计算得到的。对于每个N值，伯克霍夫正规化和焦点-焦点动力学的参数由多项式表示，其系数可以用计算机代数系统迭代计算；不需要积分，例如计算共振正规形式的作用角变量所需的积分。 我们还提供了一些数值示例，展示了该方法在代表太阳-地球和太阳-木星情况的质量参数值下的应用。 显示英文摘要

摘要： A gravitational close encounter of a small body with a planet may produce a substantial change of its orbital parameters which can be studied using the circular restricted three-body problem. In this paper we provide parametric representations of the fast close encounters with the secondary body of the planar CRTBP as arcs of non-linear focus-focus dynamics. The result is the consequence of a remarkable factorization of the Birkhoff normal forms of the Hamiltonian of the problem represented with the Levi-Civita regularization. The parametrizations are computed using two different sequences of Birkhoff normalizations of given order N. For each value of N, the Birkhoff normalizations and the parameters of the focus-focus dynamics are represented by polynomials whose coefficients can be computed iteratively with a computer algebra system; no quadratures, such as those needed to compute action-angle variables of resonant normal forms, are needed. We also provide some numerical demonstrations of the method for values of the mass parameter representative of the Sun-Earth and the Sun-Jupiter cases.