The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

检测具有多个海岸弧的最佳轨迹代表了空间任务分析中具有实际相关性的重要且具有挑战性的问题。本研究分析了两种此类最佳路径：（a）具有日食间隔的最短时间低推力轨迹和（b）最小燃料有限推力路径。修正的春分元素用于描述轨道动力学。问题 (a) 被表述为一个多弧优化问题，并推导出额外的、特定的多点优化必要条件。这些产生了从光到阴影的过渡（反​​之亦然）的 cosate 变量的跳跃条件。提出了一种能够强制执行所有多点条件的顺序求解方法，并在一个说明性的数值示例中成功应用。与之前的几项研究不同，不需要正则化或平均化来处理和解决问题。此外，这项工作重新审视问题 (b)，将其表述为单弧优化问题，同时强调最小燃料路径和问题 (a) 之间的实质性分析差异。该研究还证明了沿最优海岸弧的海岸变量（与分点元素相关联）的存在并提供了闭式表达式的推导。