Solar Sail Dynamics and Coning Control in Circular Orbits

Attitude dynamics of a solar sail are described relative to an orbiting local-vertical, local-horizontal frame under the influence of aerodynamic, solar, and gravity-gradient torques. The complete set of equilibria of the sail normal vector in local-vertical/local-horizontal is described as a function of sailcraft spin rate and orbit and sailcraft design parameters. These equilibria enable orbit-rate coning of the sail normal that is useful for changing orbit parameters using solar thrust. Lyapunov stability properties of the equilibria are analyzed, providing conditions for stable equilibria. Feedback control is considered for stabilization and additional damping, enabling any of the equilibria to be asymptotically stabilized. This approach enables long-term thrust-vector control in the presence of large environmental torques for significant orbit-parameter variation over time. An example of a 3 kg microsailcraft is used to illustrate the equilibrium and stability conditions and the performance of the attitude control.