Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem
Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem
复制标题
圆形限制三体问题中平衡点附近单模运动的多项式展开
DOI：
10.1007/s10569-018-9828-6
复制
发表时间：
2018
影响因子：
1.6
通讯作者：
Christian Circi
中科院分区：
文献类型：
--
作者：
Hanlun Lei;Bo Xu;Christian Circi
本文研究了圆形受限三体问题中围绕共线和三角振动点的单模运动。为了描述这些运动，我们采用不变流形方法，该方法将一对合适的自变量作为模态坐标，其余状态变量表示为它们的多项式级数。基于不变流形方法，概述了构造达到一定阶数的多项式展开式的一般过程。以地月系统为例，我们为共线平动点周围的单模态运动构造了高达十阶的多项式展开式，为围绕三角平动点的平面和垂直周期运动分别构造了高达八阶和六阶的多项式展开式。所构造的多项式展开式的应用在于它们可用于确定平衡点周围单模运动的初始状态。为了检查有效性，评估由多项式展开确定的初始状态的准确性。
In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth–Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.