# Orbital Mechanics and Formation Flying

• ID: 2719844
• Book
• 438 Pages
• Elsevier Science and Technology
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Aimed at students, faculty and professionals in the aerospace field, this book provides practical information on the development, analysis, and control of a single and/or multiple spacecraft in space. This book is divided into two major sections: single and multiple satellite motion. The first section analyses the orbital mechanics, orbital perturbations, and attitude dynamics of a single satellite around the Earth. Using the knowledge of a single satellite motion, the translation of a group of satellites called formation flying or constellation is explained. Formation flying has been one of the main research topics over the last few years and this book explains different control approaches to control the satellite attitude motion and/or to maintain the constellation together. The control schemes are explained in the discrete domain such that it can be easily implemented on the computer on board the satellite. The key objective of this book is to show the reader the practical and the implementation process in the discrete domain.

- Explains the orbital motion and principal perturbations affecting the satellite- Uses the Ares V rocket as an example to explain the attitude motion of a space vehicle- Presents the practical approach for different control actuators that can be used in a satellite

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Dedication

List of figures

List of tables

List of symbols

Acknowledgements

Preface

Chapter 1: Introduction

1.1 Introduction to the book

1.2 Book division

Chapter 2: Two body orbital motion

Abstract:

2.1 Introduction to orbital motion

2.2 Constraints and generalized coordinates

2.3 Lagrange's equation

2.4 System of particles

2.5 Two body orbital motion problem

2.6 Orbital equations of motion

2.7 Energy and velocity of orbiting bodies

2.8 Escape velocity

2.9 Earth Coordinate Inertial (ECI) system

2.10 Period of an orbit

2.11 Development of Kepler's equation

2.12 Suggested problems

Chapter 3: Orbital perturbations in the two body motion

Abstract:

3.1 Introduction to disturbance effects

3.2 Lagrange planetary equations

3.3 Perturbation due to the earth oblateness

3.4 The near-Earth atmosphere effects

3.6 Other disturbance effects

3.7 Suggested problems

Chapter 4: Frame rotations and quaternions

Abstract:

4.1 Introduction to rotations and quaternions

4.2 Two-dimensional frame rotations

4.3 Three-dimensional frame rotations

4.4 Example of frame rotations

4.5 Quaternion definition and rotations

4.6 Quaternion to Euler angle relations

4.7 Suggested problems

Chapter 5: Rigid body motion

Abstract:

5.1 Introduction to attitude dynamics

5.2 Rate of change of a vector

5.3 Moment of inertia

5.4 Principal moments of inertia

5.5 Energy formulation

5.6 Rate of change of a quaternion

5.7 Ares V equations of motion

5.8 Suggested problems

Chapter 6: Environmental and actuator torques

Abstract:

6.1 Introduction to torque formulation

6.2 Environmental torques

6.3 Actuator (or control) torques

6.4 Suggested problems

Chapter 7: Continuous and digital control systems

Abstract:

7.1 Introduction to methods of designing continuous and discrete control systems

7.2 Ares V equations of motion for first stage flight

7.3 Continuous control formulation

7.4 Discrete control formulation

7.6 Suggested problems

Chapter 8: Example

Abstract:

8.1 Introduction to examples in spacecraft attitude dynamics and control

8.2 Nanosatellite problem definition

8.3 B-dot controller for fast corrections

8.4 Linear quadratic regulator for attitude correction

8.5 Linear quadratic regulator control weight design

8.6 Suggested problems

Chapter 9: Formation flying

Abstract:

9.1 Introduction to formation flying

9.2 Tschauner-Hempel formulation

9.3 Clohessy-Wiltshire formulation

9.4 Earth oblateness and solar effects in formation flying

9.5 Lawden solution

9.6 Discrete optimal control problem for formation flying

9.7 Formation flying controller implementation

9.8 Suggested problems

Chapter 10: Deployment procedure for a constellation

Abstract:

10.2 Desired conditions of the satellites in the proposed tetrahedron constellation

10.3 Transfer from a circular orbit to the elliptical orbit (stage 1)

10.4 Station-keeping procedure (stage 2)

10.5 Deployment procedure for the tetrahedron constellation

10.6 Remarks

10.7 Suggested problems

Chapter 11: Reconfiguration procedure for a constellation

Abstract:

11.1 Introduction to the reconfiguration process of a constellation

11.2 Data mining process of the Lagrange planetary equations

11.3 Fuzzy logic controller

11.4 Phase I to II in-plane motion fuzzy logic control system

11.5 Phase II to III in-plane motion fuzzy logic controller

11.6 Out-of-plane motion correction

11.7 Some solutions for the reconfiguration procedures

11.8 Implementation of the fuzzy logic controller

11.9 Adaptive control scheme for reconfiguration procedure

11.10 Remarks

11.11 Suggested problems

Appendix: Formulae relating to orbital mechanics

Index

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