Attitude and orbit coupling of planar helio-stable solar sails

The coupled attitude and orbit dynamics of solar sails is studied. The shape of the sail is a simplified quasi-rhombic pyramid that provides the structure helio-stability properties. After adimensionalization, the system is put in the form of a fast-slow dynamical system where the different timescales are explicitly related to the physical parameters of the system. The orientation of the body frame with respect to the inertial orbit frame is a fast phase that can be averaged out. This gives rise to a simplified formulation that only consists of the orbit dynamics perturbed by a flat sail with fixed attitude perpendicular to the direction of the sunlight. The results are exemplified using numerical simulations.