Three-dimensional Lagrangian Coherent Structures in the Elliptic-Restricted Three-body Problem

Abstract

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.