Traditionally, the convergent solution obtained by using the methods of
optimal trajectory analysis, such as gradient methods or optimal parameter
methods, is very difficult to be proved to be unique. To overcome this
difficulty, in this paper, the state variables of the equations of motion are divided into many segments which are connected by nodes and the
minimum-time flight trajectory between each pair of neighbor nodes is
computed. After the times of flight between all pairs of neighbor nodes are computed, the dynamic programming method is employed to determine the
intermediate nodes which are to be passed through by the optimal trajectory.The global optimal trajectory is then obtained by connecting the initial node,all the intermediate nodes, and the final nodes. To validate the theory, a benchmark minimum time-to-climb problem is solved in this paper.Trajectories obtained by using the dynamic programming method are shown to have the same trend as compared to those obtained by using the traditional second-order gradient method.