This monograph investigates the trajectory optimization problems of low- and finite-thrust aerospace vehicles and spacecraft using an indirect method based on the Pontryagin maximum principle, providing a methodological basis for the construction of numerical techniques that are superior in versatility and accuracy to direct methods.This book provides a theoretical explanation of the approaches used and also an extensive gallery of the results of practical numerical studies. The problem of boundary value problem convergence has been largely overcome, which has made it possible to practically automate the optimization of trajectories and to achieve a qualitative generalization with a number of fundamentally new results. Examples of practical optimization of branching trajectories of complex dynamics systems with finite and continual sets of branches, in deterministic and stochastic statements, with control constraints and phase constraints of various orders are demonstrated.An emphasis is placed on the consistent application of methods of numerical continuation with respect to a parameter to solve various problems in the flight mechanics of spacecraft with an electric propulsion system (EPS). The problems considered include the optimization of direct interplanetary flights of spacecraft with thrusters having limited power or limited thrust, of interplanetary flights of such spacecraft using gravity assisted maneuvers, of multi-orbit interorbital transfers of spacecraft with limited-thrust EPS. As a result, it was possible to develop a set of numerical continuation methods for solving a wide range of optimization problems for spacecraft trajectories with EPS with improved characteristics in terms of convergence and performance.This monograph also contains a description of many pitfalls in solving a wide range of problems of optimizing the trajectories of aerospace vehicles and recipes for effectively overcoming them.

This monograph investigates the trajectory optimization problems of low- and finite-thrust aerospace vehicles and spacecraft using an indirect method based on the Pontryagin maximum principle, providing a methodological basis for the construction of numerical techniques that are superior in versatility and accuracy to direct methods.This book provides a theoretical explanation of the approaches used and also an extensive gallery of the results of practical numerical studies. The problem of boundary value problem convergence has been largely overcome, which has made it possible to practically automate the optimization of trajectories and to achieve a qualitative generalization with a number of fundamentally new results. Examples of practical optimization of branching trajectories of complex dynamics systems with finite and continual sets of branches, in deterministic and stochastic statements, with control constraints and phase constraints of various orders are demonstrated.An emphasis is placed on the consistent application of methods of numerical continuation with respect to a parameter to solve various problems in the flight mechanics of spacecraft with an electric propulsion system (EPS). The problems considered include the optimization of direct interplanetary flights of spacecraft with thrusters having limited power or limited thrust, of interplanetary flights of such spacecraft using gravity assisted maneuvers, of multi-orbit interorbital transfers of spacecraft with limited-thrust EPS. As a result, it was possible to develop a set of numerical continuation methods for solving a wide range of optimization problems for spacecraft trajectories with EPS with improved characteristics in terms of convergence and performance.This monograph also contains a description of many pitfalls in solving a wide range of problems of optimizing the trajectories of aerospace vehicles and recipes for effectively overcoming them.