The phenomenon of mean-motion resonance overlapping, which generates heteroclinic connections between unstable resonant orbits, is known to be crucial for the generation of large-scale chaos and global instability in celestial systems. This instability in turn can be profitably leveraged for the purposes of low-energy space mission trajectory design. In most prior work leveraging such phenomena, though, connections were found between orbits resonant with the same moon; however, both Jupiter and Saturn have multiple moons, each having their own set of mean motion resonances. This study will present some results from a search for trajectories between orbits resonant with different Jovian moons, namely Ganymede and Europa. For this, the appropriate model to use is a concentric circular restricted 4-body model, where most unstable mean-motion resonant orbits correspond to 2D tori in a 5D extended phase space. We use GPU-assisted tools inspired by collision detection algorithms from computer graphics to rapidly find near-intersections of Jupiter–Ganymede and Jupiter–Europa resonant orbit manifolds, which correspond to potential transfers. We find the Jupiter–Ganymede 4:3 resonance to be the most promising candidate for trajectories to the key 3:4 Jupiter–Europa resonance, and thus further investigate the properties of 4:3 Jupiter–Ganymede orbits.

平均运动共振重叠现象会在不稳定共振轨道之间产生异宿连接，这对于天体系统中大规模混沌和全局不稳定的产生至关重要。反过来，这种不稳定性可以被有利地用于低能量太空任务轨迹设计的目的。然而，在大多数利用此类现象的先前工作中，发现了与同一个卫星共振的轨道之间的联系。然而，木星和土星都有多个卫星，每个卫星都有自己的一组平均运动共振。这项研究将展示一些搜索与不同木星卫星（即木卫三和木卫二）共振的轨道之间的轨迹的结果。为此，合适的模型是同心圆受限四体模型，其中最不稳定的平均运动共振轨道对应于 5D 扩展相空间中的 2D 环面。我们使用受计算机图形学碰撞检测算法启发的 GPU 辅助工具，快速找到木星-木卫三和木星-欧罗巴共振轨道流形的近交点，这些交点对应于潜在的转移。我们发现木星-木卫三 4:3 共振是关键 3:4 木星-欧罗巴共振轨道最有希望的候选者，因此进一步研究 4:3 木星-木卫三轨道的特性。