The electric solar wind sail (E-sail) has been proposed as a novel propulsion system that, if successful, promises to facilitate missions that would be inconvenient or impractical with traditional chemical propellants. The most common E-sail concept includes a central hub with several long positively charged tethers extending radially outward that harvest momentum from protons in the solar wind. Before the technology is ready for a demonstration mission, we must prove E-sail dynamics can be controlled throughout all phases of the mission. The objective of this paper is to present an analytical model for the linear vibrations of hub and spoke E-sails to facilitate the development of necessary control schemes. Although there is no limit to the number of spokes in our model, we demonstrate its capability by representing a system with 3 spokes. The resultant natural frequencies and mode shapes provide insight into the dynamics and stability of E-sails and lay the foundation for development of control schemes. In addition, our work reveals several simple calculations that accurately estimate many of the natural frequencies and could be used to facilitate the design of future E-sails.

有人提出将电动太阳风帆（E-sail）作为一种新型的推进系统，如果成功的话，有望促进传统化学推进剂不方便或不切实际的飞行任务。最常见的电子帆概念包括一个中心轮毂，该中心轮毂带有多个径向延伸的带正电的长链，可从太阳风中的质子中获取动量。在该技术准备用于演示任务之前，我们必须证明在整个任务的所有阶段中都可以控制电子帆动态。本文的目的是为轮毂和辐条电子风帆的线性振动提供一个解析模型，以促进必要控制方案的开发。尽管模型中的辐条数量没有限制，但我们通过表示一个具有3个辐条的系统来证明其功能。由此产生的固有频率和模态形状可洞察电子帆的动态和稳定性，并为开发控制方案奠定基础。此外，我们的工作还揭示了一些简单的计算方法，它们可以准确地估计许多自然频率，并且可以用于简化未来电子帆的设计。