论文标题
椭圆限制的三体问题的三维拉格朗日相干结构
Three-dimensional Lagrangian Coherent Structures in the Elliptic-Restricted Three-body Problem
论文作者
论文摘要
在空间任务的初步设计中，确定驱动系统行为的动态区域或在质量上不同的动态区域可能很有用。拉格朗日相干结构（LCS）已被广泛用于动态系统的分析，并将稳定和不稳定的流形的概念概括为具有任意时间依赖性的系统。但是，到目前为止，在天体动力学中使用三维LC是有限的。本文介绍了作者DA-LCS引入的新数值方法的应用，以使用椭圆限制的三体问题（ER3BP）作为测试案例的天体动力学系统。我们能够直接从LC的变异理论中构建与Sun-Mars ER3BP相关的完整的三维LC，即使是为了在数值挑战性的初始条件上。详细分析了LCS，显示在这种情况下它如何在没有任何先验知识的情况下将其定性不同行为区域分开。然后，本文研究了整合时间的影响以及初始条件对发现的LCS的参数化。我们强调了在最具挑战性的测试案例中浮点算术的限制产生的圆形错误，并提供了减轻策略以避免这些错误的策略。
In the preliminary design of space missions it can be useful to identify regions of dynamics that drive the system's behaviour or separate qualitatively different dynamics. The Lagrangian Coherent Structure (LCS) has been widely used in the analysis of dynamical systems, and generalises the concept of the stable and unstable manifolds to systems with arbitrary time-dependence. However, the use of three-dimensional LCS in astrodynamics has thus far been limited. This paper presents the application of a new numerical method introduced by the authors, DA-LCS, to astrodynamics systems using the Elliptic-Restricted Three-body Problem (ER3BP) as a test case. We are able to construct the full, three-dimensional LCS associated with the Sun-Mars ER3BP directly from the variational theory of LCS even for numerically challenging initial conditions. The LCS is analysed in detail, showing how it in this case separates regions of qualitatively different behaviour without any a priori knowledge. The paper then studies the effect of integration time and the parameterisation of the initial condition on the LCS found. We highlight how round-off errors arise from limits of floating-point arithmetic in the most challenging test cases and provide mitigating strategies for avoiding these errors practically.
