# Three-Dimensional Guidance Laws for Spacecraft Propelled by a SWIFT Propulsion System
## 5 Conclusions  
This paper presented the optimal control law of a spacecraft equipped with a SWIFT in a 3D heliocentric transfer between two assigned Keplerian orbits. The proposed mathematical model extends the recent literature results on this advanced, rather exotic, propulsion system concept that allows for achieving interplanetary orbit transfer without the expenditure of a propellant and with a continuous propulsive acceleration. The thrust vector model discussed in this paper can be used to obtain the optimal control law in a wide range of mission applications. The thrust model has been used in this work to study the rapid orbit-to-orbit transfer by describing the spacecraft dynamics in terms of Cartesian vectors or orbital (both classic and equinoctial) elements. In particular, the heliocentric dynamics of the spacecraft has been modeled assuming only the effects of SWIFT-induced acceleration and the gravitational pull of the Sun. In this regard, a potential limitation of the proposed approach is represented by the absence of the inevitable orbital perturbations that can influence the shape of the optimal transfer trajectory. In this sense, a more refined model of orbital dynamics (which perhaps also includes possible uncertainties on the performance characteristics of the propulsion system) would allow for a more precise transfer trajectory.  
The simulation results show that the transfer performance of a SWIFT-based spacecraft in a 3D scenario strictly depends on the value of the design parameter \(K\). In fact, the transverse (i.e., perpendicular to the radial direction) component of the vector \(\mathbf{a}\) depends on \(K\) so that a small value of that design parameter gives a small transverse component of \(\mathbf{a}\), with the characteristic acceleration being fixed. In a 3D orbit transfer, the value of the transverse component of the vector \(\mathbf{a}\) plays an important role in achieving a short flight time, especially in mission scenarios requiring a large variation in the orbital inclination. A possible extension of this work is related to the analysis of displaced, heliocentric, non-Keplerian orbits for planetary observation using a SWIFT-propelled spacecraft. In fact, the proposed thrust vector model allows the geometric characteristics of the heliocentric displaced orbit to be obtained as a function of the two design parameters of the SWIFT system. In that context, the optimal control law obtained in the case of a spherical reference frame can be used to study the rapid transfer trajectories from the Earth's parking orbit and the target (heliocentric) displaced orbit.  
Figure 9: Results of the optimization process in a 3D Earth–Mars mission scenario when \(a_{c}=0.07\,\mathrm{mm}/\mathrm{s}^{2}\) and \(K=1\). (**a**) Time variation of the components of \(\mathbf{\hat{t}}\) in RTN. (**b**) Optimal transfer trajectory (black line). Blue line \(\rightarrow\) is Earth’s orbit; red line \(\rightarrow\) is Mars’ orbit; blue circle \(\rightarrow\) is start point; red circle \(\rightarrow\) is arrival point; blue star \(\rightarrow\) is Earth’s perihelion; red star \(\rightarrow\) is Mars’ perihelion; orange circle \(\rightarrow\) is the Sun.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The author declares no conflicts of interest.