Azimov - Analytical solutions for extremal space trajectories

First edition

Dilmurat M. Azimov

1. Tables in Chapter 4
2. Tables in Chapter 9

1. Figures in Chapter 2
2. Figures in Chapter 3
3. Figures in Chapter 4
4. Figures in Chapter 7
5. Figures in Chapter 9

Butterworth-Heinemann is an imprint of Elsevier

The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom

50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States

Copyright 2018 Dilmurat M. Azimov. Published by Elsevier Inc. All rights reserved.

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher's permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.

This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

Library of Congress Cataloging-in-Publication Data

A catalog record for this book is available from the Library of Congress

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library

ISBN: 978-0-12-814058-1

For information on all Butterworth-Heinemann publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans

Acquisition Editor: Carrie Bolger

Editorial Project Manager: Carrie Bolger

Production Project Manager: Kiruthika Govindaraju

Designer: Matthew Limbert

Typeset by VTeX

To my parents,

Mukhammadjan Azimov and Rano Azimova

This monograph intends to develop analytical and approximate-analytical methods for optimal control problem on determination of optimal and extremal trajectories in a Newtonian, linear central and uniform gravitational fields. This work then applies these methods to analytical trajectory synthesis for various maneuvers, including inter orbital, escape and planetary landing maneuvers. The results of this synthesis can be considered as the nominal or reference trajectory solutions for the development of onboard guidance and navigation schemes. Development of these schemes deserves separate studies and is beyond the scope of this work. This work aims to derive analytical solutions to the optimal control problem and demonstrate their application to the synthesis of optimal nominal or reference trajectories for autonomous space guidance. The main contents of this work include derivation of the solutions for thrust arcs, development of a methodology of analytical synthesis of optimal and extremal trajectories, determination of the number and sequence of thrust arcs on these trajectories and coordinates of switching points, analytical synthesis of nominal maneuver design trajectories and development of control laws and corresponding computational procedures for implementation of these laws.

The author wishes to express his appreciation to all friends and colleagues who provided their feedback and suggestions to improve the quality and contents of this monograph. The author thanks Mamura D. Yuldasheva who contributed to the design of the cover page by providing many interesting ideas and optional pictures of space trajectories.