Optimal Impulsive Orbital 3D Maneuver with or without Time constraint

Orbital transfers are an inevitable part of space missions. An optimal impulsive maneuver is one that consumes the minimum amount of energy to accomplish the transfer. The problem of optimal impulsive orbital 3D maneuver has been the subject of very few published researches due to its particular complications. Finding the optimized solution to this problem needs innovations in every aspect. However, this paper tries to turn this special kind of transfer into an applicable concept. In this paper, optimization equations to express the geometry of initial, target and transfer orbits with respect to each other are derived using the spherical trigonometry. Moreover, several cases for positioning the initial and target orbits relative to each other are presented. Based on actual applications, the problem is solved for both unconstrained and time-constrained cases. Comprising several local minimums is a characteristic of this optimization problem, consequently, variations of the delta-V are presented as a function of independent variables to achieve the general solution. The numerical results for the optimal impulsive orbital 3D maneuver are presented for a case study, and it is verified by comparing the results in a particular case with those from the Lambert problem. The illustrated results show the appropriate accuracy of the derived equations and performed computations.