Dynamics and control of flexible spinning solar sails under reflectivity modulation

Electrochromic devices have been used for the attitude control of a spinning solar sail in a deep space mission by modulating the reflectivity of the sail membrane. As a flexible spinning solar sail has no rigid structure to support its membrane, the distributed load due to solar radiation will lead to the deformation of the sail membrane, and the control torque generated by reflectivity modulation can introduce oscillatory motion to the membrane. By contrast, the deformation and oscillatory motion of the sail membrane have an impact on the performance of the reflectivity control. This paper investigates the dynamics and control of flexible spinning solar sails under reflectivity modulation. The static deformation of a spinning sail membrane subjected to solar radiation pressure in an equilibrium state is analyzed. The von Karman theory is used to obtain the displacements and the stress distribution in the equilibrium states. A simplified analytical first-order mode is chosen to model the membrane oscillation. The coupled membrane oscillation-attitude-orbit dynamics are considered for a GeoSail formation flying mission. The relative attitude and orbit control of flexible spinning solar sails under reflectivity modulation are numerically tested. The simulations indicate that the membrane deformation and oscillation have a lower impact on the control of the reflectivity modulated sails than the increase of the spinning rate.