Regular variables in the problem of low-thrust trajectory optimization

The regularization of spacecraft motion equations by the Kustaanheimo-Stiefel transformation for coordinates and Sundman’s transformation for time in the case of interplanetary low-thrust optimal transfer is considered. From Pontryagin’s maximum principle, the thrust vector optimal control is derived under the limited power condition. The Earth-Mars transfer problem is solved in the regular variables. The comparison of calculated trajectories with the ones obtained by the parameter continuation method is performed, and the stability properties of the two-point boundary value problem in the Cartesian and regular variables are studied.