## 1 Introduction  
Since the success of JAXA's IKAROS spacecraft, launched on 20 May 2010 [1, 2, 3], the solar sail technology has demonstrated its capabilities across a range of space mission applications [4, 5, 6]. Although the solar sail concept dates back to about a century ago thanks to the works of the Soviet pioneers of astronuatics [7, 8], the manufacture of such an advanced propulsion system and its integration with the spacecraft control and navigation system [9, 10, 11] has been completed in the last decade only, using the lessons learned from in-flight tests [12, 13, 14]. In this context, the most recent example of a spacecraft propelled by a solar sail is NASA's Near-Earth Asteroid Scout (NEA Scout) [13, 15], which is a 6U CubeSat that was arranged as a secondary payload for the maiden flight of the Space Launch System (SLS) in the middle of November 2022. Unfortunately, the ground station failed to establish communications with the solar sail CubeSat after its successful separation from the SLS so that the NEA Scout is currently considered lost. The next attempt to analyze the in-flight performance of a solar sail will be at the beginning of 2025, when NASA's Solar Cruiser will start its deep-space scientific mission for Sun observations [14, 16]. One of the most delicate aspects of a solar sail-based mission, both from the trajectory design and the station-keeping viewpoint, is its attitude control [17], which requires a large reflective surface to be oriented along a given space direction [18, 19] to obtain a suitable thrust vector [20, 21]. The simplest solution to avoid any sail reorientation maneuver is the adoption of a Sun-facing attitude [22, 23], which is a configuration where the sail nominal plane is always perpendicular to the Sun-spacecraft line (referred to as radial direction), which coincides with the direction of propagation of the Sun's photons. It is known, in fact, that a Sun-facing attitude may be passively maintained in an orbital reference frame by means of an axially symmetric sail [24, 25] with a slightly conical reflective surface, whose apex is oriented toward the Sun [26]. In that case, however, if the sail film is designed to be close to an ideal surface with specular reflection [27], a solar sail with a Sun-facing attitude is able to give only a radial thrust vector [28] and, as such, it is unable to change the spacecraft angular momentum [26]. Nevertheless, a solar sail with a Sun-facing attitude is used in important space applications such as, for example, the generation of artificial equilibrium points in the (Earth + Moon)-Sun system [29, 30, 31]. As far as orbit transfers are concerned, a solar sail with a Sun-facing attitude may be employed only in a few cases of two-dimensional mission scenarios, such as the transfer between two Keplerian orbits that share the same value of semilatus rectum [23, 32], or the (heliocentric) deployment of a smart dust swarm [33, 34, 35]. However, a Sun-facing attitude is unsuited for transfers between two generic Keplerian orbits, even in the simplified case of coplanar orbits or if the propulsive acceleration magnitude is modulated during the flight. In principle, a thrust vector magnitude modulation is possible by means of electrohromic panels installed on the sail surface [36, 37, 38, 39], or through the rotation of long reflective blades, as it happens in a Heliogyro configuration [40, 41, 42]. The latter concept was originally conceived about 50 years ago within the ambitious proposal of a rendezvous mission to [PERSON]'s comet [43], and it has recently received new attention [22, 44, 45] due to its peculiarities in terms of thrust vector control. A possible solution to the problem of changing the orbital angular momentum with a solar sail in a Sun-facing configuration is offered by a diffractive sail, whose concept has been recently proposed by [PERSON] [46, 47, 48].