Nonsingular Quaternion Formulation for All-electric Radiation Minimization Trajectories

While previous methods for trajectory optimization have allowed for minimization of time, past efforts have fallen short with regard to the minimization of radiation exposure. This is in part due to the numerical sensitivity of the optimization and the utilization of coordinates that are singular at the poles. In this method, a quaternion formulation is utilized in order to provide nonsingular coordinates and is coupled with a second-order Sundman transformation in order to improve the numerical performance. This formulation is used to obtain the optimal trajectory that minimizes the radiation damage in a low-thrust orbit-raising mission scenario.