Modal Analysis of Electric sail

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.