Dynamic Modeling and Stability Analysis for Spinning Circular Solar Sail Considering Periodically Time-Varying Characteristics

The spinning circular solar sail is a promising spacecraft for long-duration missions. This work reveals its structural dynamic and stability behavior under the periodically time-varying solar radiation pressure and gravitational force. The geometric stiffness generated by the centrifugal force due to spinning and the coupling effect between the deformation and solar radiation pressure are taken into account. The von Kármán plate theory is adopted by neglecting the high-frequency in-plane vibrations and considering the effect of the in-plane internal force on the transverse vibration. The partial differential equation of the spinning solar sail is derived and further spatially discretized into periodically time-varying equations of motion. Effects of Poisson ratio and radius ratio on natural frequencies and mode shapes are analyzed, and curve veering phenomena are then observed. Steady-state periodic responses of the solar sail under the solar radiation pressure with different orbit distances, incident angles, and spinning angular velocities are analyzed. The stability analysis is rigorously performed by the Floquet theory rather than the commonly used approach of conducting the eigenvalue analysis at a series of specific discrete time nodes. Moreover, the stability boundary associated with transverse vibrations is determined, which contributes to the parameter design of the spinning solar sail.