Modified shape-based method for three-dimensional trajectory design

Although the shape-based method has been proven to be useful for low-thrust trajectory design,and be capable to provide near-optimal solution for a more accurate trajectory optimization method,it is slightly non-effective when used in some 3D cases.In this paper,a modified 3D shape-based method is proposed for earth trajectory design.In this approach,in consideration of the sinusoidal periodic variation in z direction of actual trajectory,a new exponential sinusoid model is chosen for the out-of-plane motion,with four coefficients such that four scalar out-of-plane boundary conditions can be satisfied.After deriving the 3D shape-based procedure,low-thrust trajectory design example with modest inclination change is given.The results demonstrate that this modified approach is feasible for the transfer trajectory design,and comparing to the former shape-based method,the z direction solution is more coincident with the actual situation,furthermore,the solution may be used for further mission planning,trajectory evaluation and optimization.