Analysis of Degree of Controllability based on Gramian for Solar Sails in Artificial Lagrangian Orbits

The model of the solar sail in the Sun-Earth system is established, the concept of degree of controllability based on controllability Gramian is introduced as well. The degree of controllability of solar sail at five artificial Lagrangian points near the sun-earth L
₁
point, and the degree of controllability of solar sail at one chosen artificial Lagrangian point under different cases of control inputs are evaluated. The results reveal that the controllability of the solar sail is various due to the different locations and the distinct control inputs. The results could give us more quantitative information about the controllability of solar sail, rather than it is simply controllable or not, which may provide more effective suggestions for the design of the solar sail in the future space missions.