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About this book

This book consolidates decades of knowledge on space flight navigation theory, which has thus far been spread across various research articles. By gathering this research into a single text, it will be more accessible to students curious about the study of space flight navigation. Books on optimal control theory and orbital mechanics have not adequately explored the field of space flight navigation theory until this point.
The opening chapters introduce essential concepts within optimal control theory, such as the optimization of static systems, special boundary conditions, and dynamic equality constraints. An analytical approach is focused on throughout, as opposed to computational. The result is a book that emphasizes simplicity and practicability, which makes it accessible and engaging. This holds true in later chapters that involve orbital mechanics, two-body maneuvers, bounded inputs, and flight in non-spherical gravity fields.
The intended audience is primarily upper-undergraduate students, graduate students, and researchers of aerospace, mechanical, and/or electrical engineering. It will be especially valuable to those with interests in spacecraft dynamics and control. Readers should be familiar with basic dynamics and modern control theory. Additionally, a knowledge of linear algebra, variational methods, and ordinary differential equations is recommended.

Table of Contents


Chapter 1. Introduction

Navigating a space vehicle consists of first determining and then steering a desired path under the gravitational influence of several large bodies.
Ashish Tewari

Chapter 2. Analytical Optimal Control

Optimization refers to the process of achieving the best possible result (objective), given the circumstances (constraints). When applied to determine a control strategy for fulfilling a desired task, such an optimization is called optimal control .
Ashish Tewari

Chapter 3. Orbital Mechanics and Impulsive Transfer

Orbital mechanics refers to the study of the translational motion of bodies in mutual gravitational attraction, and the resulting spatial paths of the centers of mass of the respective bodies are called the orbits. The relative motion of two spherical bodies in mutual gravitational attraction is the fundamental problem of translational space dynamics, called the two-body problem (or the Keplerian motion), and possesses an analytical solution.
Ashish Tewari

Chapter 4. Two-Body Maneuvers with Unbounded Continuous Inputs

A majority of spacecraft navigation problems involve transfers between two given positions and velocities. When continuous inputs are applied for the orbital transfer of a spacecraft around a central body, the perturbed two-body model can be used as a plant to derive the optimal trajectory and control history.
Ashish Tewari

Chapter 5. Optimal Maneuvers with Bounded Inputs

Spacecraft engines can generate only limited thrust magnitudes. This implies that the acceleration inputs in space navigation must necessarily be bounded. The trajectory optimization must therefore be performed taking bounded inputs into account. As discussed in the earlier chapters, the nature of optimal trajectories with bounded acceleration inputs can be classified as either impulsive thrust or continuous thrust maneuvers.
Ashish Tewari

Chapter 6. Flight in Non-spherical Gravity Fields

Spaceflight involving orbital transfers around irregularly shaped bodies or in the gravity field of several large bodies is fundamentally different from the flight in the gravity field of a single spherical body, which was covered in the previous chapters. The primary reason for this difference is that the spacecraft is no longer in a time-invariant gravity field of the two-body problem, but instead encounters a time-dependent field due to the relative motion of the multiple large bodies with respect to one another, or due to the changing position of the spacecraft relative to a rotating, non-spherical body.
Ashish Tewari


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