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Analytical Solutions for Extremal Space Trajectories presents an overall treatment of the general optimal control problem, in particular, the Mayer's variational problem, with necessary and sufficient conditions of optimality. It also provides a detailed derivation of the analytical solutions of these problems for thrust arcs for the Newtonian, linear central and uniform gravitational fields. These solutions are then used to analytically synthesize the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers. Many numerical examples utilizing the proposed analytical synthesis of the space trajectories and comparison analyses with numerically integrated solutions are provided. This book will be helpful for engineers and researchers of industrial and government organizations, and is also a great resource for university faculty and graduate and undergraduate students working, specializing or majoring in the fields of aerospace engineering, applied celestial mechanics, and guidance, navigation and control technologies, applied mathematics and analytical dynamics, and avionics software design and development.