Application of the Angular Independent Variable and Its Regularizing Transformation in the Problems of Optimizing Low-Thrust Trajectories

Аннотация

The expediency of using the true longitude or the associated angle as an independent variable in the problems of optimizing multi-revolution, low-thrust trajectories of spacecraft is considered. The auxiliary longitude is introduced, which is used further as a new independent variable instead of time. The advantage of using the auxiliary longitude as an independent variable in the problem of optimizing the trajectories with a fixed angular range and optimum transfer time is demonstrated. The problems of optimizing the trajectories of spacecraft with an ideally controlled, limited-power engine and a limited-thrust engine with a constant exhaust velocity are considered. The possibility of improving the convergence of the methods of solving the problems of optimizing the trajectories with a limited-thrust engine is considered. This improvement is achieved by joint utilization of the smoothing approximation of a relay thrust-switching function and the regularizing transformation of an independent variable, which extends the switching function values in the vicinity of thrust switching instants. Based on the results, the method for solving the problems of optimizing multi-revolution transfers is proposed; the numerical examples of its application are presented.