Abstract This paper proposes a novel description of the equations of motion for low-thrust trajectory design in the presence of a third-body perturbation. The framework is formulated using Gauss’ Variational Equations (GVE) with two distinct accelerations: the one produced by the electric engine and the disturbing term of the third-body effect, which is computed using the disturbing potential of the previously studied Keplerian Map. The presented GVE third-body (GVE-3B) framework allows for a simple and intuitive description of the low-thrust optimisation problem. It is accurate until very close to the sphere of influence of the perturbing body, and thus can be used to target trajectories in low-energy regimes. Together with the framework, this paper develops a methodology to generate low-energy first-guess solutions for low-thrust trajectories. Both the methodology and the framework are showcased in the design of two distinct missions: a rendezvous with asteroid 2017 SV19 during its next Earth encounter, after departing from the unstable invariant manifold of the L 2 point in the Sun-Earth system, and the capture of asteroid 2018 AV2 to a stable invariant manifold of the same point.

中文翻译：

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使用变分方程的低能量状态下的低推力轨迹设计

摘要 本文提出了在存在第三体扰动的情况下低推力轨迹设计的运动方程的新描述。该框架是使用具有两种不同加速度的高斯变分方程 (GVE) 制定的：一种是由电动发动机产生的，另一种是使用先前研究的开普勒地图的干扰势计算的第三体效应的干扰项。提出的 GVE 第三体 (GVE-3B) 框架允许对低推力优化问题进行简单直观的描述。它在非常接近扰动体的影响范围之前是准确的，因此可用于在低能量状态下瞄准轨迹。与该框架一起，本文开发了一种方法来为低推力轨迹生成低能量的第一猜测解决方案。