论文标题
航天器轨迹设计的庞加莱地图拓扑的提取和可视化
Extraction and Visualization of Poincaré Map Topology for Spacecraft Trajectory Design
论文作者
论文摘要
任务设计师必须研究许多动态模型，以计划满足任务限制的低成本航天器轨迹。他们通常使用庞加莱地图在多体重力系统中发现的周期性轨道和不变形流形的互连网络搜索合适的路径。本文涉及对这种结构景观的提取和交互式视觉探索，以帮助航天器轨迹计划。我们提出了算法解决方案，以解决天体动力学问题中拓扑表征的特定挑战，并允许对所得信息进行有效的视觉分析。该可视化框架应用于圆形限制的三体问题（CR3BP），在该问题中，它以合适的格式以适合交互式转移选择的格式揭示了新型的周期轨道。代表性设计问题说明了航天器路径计划者如何利用我们的拓扑可视化来充分利用节能轨迹设计的自然动力学途径。
Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincaré maps to search for a suitable path through the interconnected web of periodic orbits and invariant manifolds found in multi-body gravitational systems. This paper is concerned with the extraction and interactive visual exploration of this structural landscape to assist spacecraft trajectory planning. We propose algorithmic solutions that address the specific challenges posed by the characterization of the topology in astrodynamics problems and allow for an effective visual analysis of the resulting information. This visualization framework is applied to the circular restricted three-body problem (CR3BP), where it reveals novel periodic orbits with their relevant invariant manifolds in a suitable format for interactive transfer selection. Representative design problems illustrate how spacecraft path planners can leverage our topology visualization to fully exploit the natural dynamics pathways for energy-efficient trajectory designs.
