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.

Features an analyses of Pontryagin extremals and/or Pontryagin minimum in the context of space trajectory design Presents the general methodology of an analytical synthesis of the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers Assists in developing the optimal control theory for applications in aerospace technology and space mission design

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.- Features an analyses of Pontryagin extremals and/or Pontryagin minimum in the context of space trajectory design- Presents the general methodology of an analytical synthesis of the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers- Assists in developing the optimal control theory for applications in aerospace technology and space mission design

This book explores the reconstruction, extension, and enhancement of the Apollo targeting and guidance algorithms, integrating original guidance concepts with new analytical solutions. It details the Apollo ground-based and on-board algorithms, their iterative targeting procedures, and their performance in post-flight mission reconstructions. The book further introduces advanced real-time targeting methods that improve landing accuracy and autonomy, supporting future robotic and human lunar landing missions. By eliminating iterative computations, these solutions enable real-time re-targeting during powered descent, ensuring safer and more precise landings. This work bridges past Apollo-era methods with modern advancements, making it essential for undergraduate and graduate students, aerospace engineers, researchers, and mission designers.

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.

Features an analyses of Pontryagin extremals and/or Pontryagin minimum in the context of space trajectory design Presents the general methodology of an analytical synthesis of the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers Assists in developing the optimal control theory for applications in aerospace technology and space mission design

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.- Features an analyses of Pontryagin extremals and/or Pontryagin minimum in the context of space trajectory design- Presents the general methodology of an analytical synthesis of the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers- Assists in developing the optimal control theory for applications in aerospace technology and space mission design

This book explores the reconstruction, extension, and enhancement of the Apollo targeting and guidance algorithms, integrating original guidance concepts with new analytical solutions. It details the Apollo ground-based and on-board algorithms, their iterative targeting procedures, and their performance in post-flight mission reconstructions. The book further introduces advanced real-time targeting methods that improve landing accuracy and autonomy, supporting future robotic and human lunar landing missions. By eliminating iterative computations, these solutions enable real-time re-targeting during powered descent, ensuring safer and more precise landings. This work bridges past Apollo-era methods with modern advancements, making it essential for undergraduate and graduate students, aerospace engineers, researchers, and mission designers.