This study examines the impact of electric solar wind sail (E-sail) parameters on the attitude stability of E-sail's central spacecraft by using a comprehensive rigid-flexible coupling dynamic model. In this model, the nodal position finite element method is used to model the elastic deformation of the tethers through interconnected two-node tensile elements. The attitude dynamics of the central spacecraft is described using a natural coordinate formulation. The rigid-flexible coupling between the central spacecraft and its flexible tethers is established using Lagrange multipliers. Our research reveals the significant influences of parameters such as tether numbers, tether's electric potential, and solar wind velocity on attitude stability. Specifically, solar wind fluctuations and the distribution of electric potential on the main tethers considerably affect the attitude stability of the spacecraft. For consistent management, the angular velocities of the spacecraft must remain at target values. Moreover, the attitude stability of a spacecraft has a pronounced dependence on the geometrical configuration of the E-sail, with axisymmetric E-sails proving to be more stable.