Attitude dynamics of an electric sail model with a realistic shape

The Electric Solar Wind Sail is an innovative propulsion system that gains thrust from the interaction of the incoming ions from the solar wind with an artificial electric field produced by means of long charged tethers, which are deployed and maintained stretched by rotating the spacecraft around a spin axis. Under the combined interaction between solar wind dynamic pressure and centrifugal force, the tethers reach an equilibrium configuration whose spatial shape must be known for obtaining a reasonable estimate of the propulsive acceleration, a fundamental information for preliminary mission analysis purposes. This problem has been addressed in recent papers, which deal with the analytical expressions of thrust and torque vectors of a spinning and axially-symmetric Electric Solar Wind Sail. The torque acting on the sail induces a perturbation on the orientation of the thrust vector, which is here studied by analyzing the attitude dynamics. Numerical simulations show that the spacecraft motion is characterized by an undamped precession combined with a nutation motion. The effect due to the torque acting on the spacecraft is to align the thrust direction along the Sun-sail line, thus reducing the maneuvering capabilities. This paper proposes an effective control law which is able to remove the torque by suitably adjusting the tether electric voltage. It is shown that the proposed solution maintains the nominal thrust magnitude, and requires a small electric voltage modulation.