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Solar sails are large and lightweight reflective structures that are propelled by solar radiation pressure. This chapter covers their orbital and attitude dynamics and control. First, the advantages and limitations of solar sails are discussed and their history and development status is outlined. Because the dynamics of solar sails is governed by the (thermo-)optical properties of the sail film, the basic solar radiation pressure force models have to be described and compared before parameters to measure solar sail performance can be defined. The next part covers the orbital dynamics of solar sails for heliocentric motion, planetocentric motion, and motion at Lagrangian equilibrium points. Afterwards, some advanced solar radiation pressure force models are described, which allow to quantify the thrust force on solar sails of arbitrary shape, the effects of temperature, of light incidence angle, of surface roughness, and the effects of optical degradation of the sail film in the space environment. The orbital motion of a solar sail is strongly coupled to its rotational motion, so that the attitude control of these soft and flexible structures is very challenging, especially for planetocentric orbits that require fast attitude maneuvers. Finally, some potential attitude control methods are sketched and selection criteria are given.
Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.