## 2 Thrust Vector Description and Mathematical Model  
This section is substantially divided into three parts. The first one concerns the description of the thrust vector of the Sun-facing diffractive sailcraft and the definition of the single (binary) scalar control variable. In this context, the paper resorts to the results of the literature limiting the discussion to the description of the vectorial expression that allows for writing the propulsive acceleration of a diffractive sailcraft equipped with a set of electro-optically controlled panels. Additional comments regarding the origin of that simplified thrust model can be found in the recent work of the author [32] and in the seminal paper by [PERSON] [2].  
The obtained thrust vector's expression is then used in the second part of the section to write the nonlinear equations of motion of the Sun-facing diffractive sailcraft in a two-dimensional, heliocentric, mission scenario. In this case, a classical polar reference frame was used, while the boundary conditions were calculated considering the non-zero eccentricity of the elliptical reference orbit. The mathematical model used in that part of the section to describe the heliocentric dynamics of the diffractive sailcraft is consistent with the approach commonly employed in the preliminary design of interplanetary missions [43]. In particular, this method allows the designer to explore a wide range of possible transfer trajectories with reduced computational effort. Naturally, a subsequent and more refined mission analysis requires a detailed description of the spacecraft dynamics, in which, for example, both perturbations and possible uncertainties in the thrust vector are taken into account.  
The third and last part of this section instead describes the mathematical model used to determine the optimal control law (in implicit form) and the transfer trajectory in an assigned phasing maneuver. In that context, indeed, a typical optimization model has been employed, as usually happens in problems of this type, in order to determine the nominal performances (i.e., in the absence of uncertainties and perturbations) of the Sun-facing diffractive sailcraft. Additionally, in this case, the discussion is reduced to the essential part of the model in order to allow the reader to have the entire mathematical model available for the reproduction of the numerical results described in Section 3. Being an optimization approach well known in the literature [44] and largely validated in many mission scenarios [45], the last part of this section omits specific comments on the meaning of some steps, referring to recent bibliographical references [32].  
The proposed approach, in which the sailcraft orientation is maintained Sun-facing throughout the entire interplanetary transfer, can be extended, with minor modifications to the mathematical model, to the more general case of a piecewise constant steering law, where the sail's attitude assumes a finite set of discrete orientations. In this context, the recent work by [PERSON] et al. [46] analyzes the optimal transfer of a spacecraft propelled by a conventional continuous-thrust propulsion system, employing an elegant analytical method that enables the sensitivity matrix to be derived in closed form, thereby reducing computational effort during the trajectory optimization.