Spacecraft Dynamics

454 Pages·2005·56.468 MB·English

by  T. Kane, et al.

SPACECRAFT
DYNAMICS
Thomas R. Kane, Peter W Likins,.
and David A. Levinson
Spacecraft Dynamics
Thomas R. Kane, Stanford University
Peter W. Likins, Lehigh University
David A. Levinson, Lockheed Palo Alto Research Laboratory
Copyright 2005 by the authors
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McGraw-Hill Book Company, 1993
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Ithaca, N.Y.
January 2005
£NGJN. MOV 1 1982
CORNELL UNIVERSITY
LIBRARIES
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SPACECRAFT
DYNAMICS
Thomas R. Kane
Stanford University
Peter W. Likins
Lehigh University
David A. Levinson
Lockheed Palo Alto Research Laboratory
McGraw-Hill Book Company
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SPACECRAFT DYNAMICS
Copyright © 1983 by McGraw-Hill, Inc. All rights reserved.
Printed in the United States of America. Except as permitted under
the United States Copyright Act of 1976, no part of this publication may
be reproduced or distributed in any form or by any means, or stored
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of the publisher.
1234567890 HDHD 898765432
ISBN 0-Q7-Q37flM3-b
Library of Congress Cataloging in Publication Data
Kane, Thomas R.
Spacecraft dynamics.
Includes index.
1. Space vehicles—Dynamics. I. Likins, Peter W.
II. Levinson, David A. III. Title.
TL1050.K36 629.47'0r53111 81-8431
ISBN 0-07-037843-6 AACR2
j>
CONTENTS
Preface vii
To the Reader xi
Chapter 1 Kinematics 1
1.1 Simple Rotation 1
1.2 Direction Cosines 4
1.3 Euler Parameters 12
1.4 Rodrigues Parameters 16
1.5 Indirect Determination of Orientation 20
1.6 Successive Rotations 23
1.7 Orientation Angles 30
1.8 Small Rotations 38
1.9 Screw Motion 42
.10 Angular Velocity Matrix 47
.11 Angular Velocity Vector 49
.12 Angular Velocity Components 53
.13 Angular Velocity and Euler Parameters 58
.14 Angular Velocity and Rodrigues Parameters 62
.15 Indirect Determination of Angular Velocity 68
.16 Auxiliary Reference Frames 71
.17 Angular Velocity and Orientation Angles 73
.18 Slow, Small Rotational Motions 78
.19 Instantaneous Axis 81
.20 Angular Acceleration 84
l.21 Partial Angular Velocities and Partial Velocities 87
iii
iv CONTENTS
Chapter 2 Gravitational Forces
2.1 Gravitational Interaction of Two Particles
2.2 Force Exerted on a Body by a Particle
2.3 Force Exerted on a Small Body by a Particle
2.4 Force Exerted on a Small Body by a Small Body
2.5 Centrobaric Bodies
2.6 Moment Exerted on a Body by a Particle
2.7 Moment Exerted on a Small Body by a Small Body
2.8 Proximate Bodies
2.9 Differentiation with Respect to a Vector
2.10 Force Function for Two Particles
2.11 Force Function for a Body and a Particle
2.12 Force Function for a Small Body and a Particle
2.13 Force Function in Terms of Legendre Polynomials
2.14 Force Function for Two Small Bodies
2.15 Force Function for a Centrobaric Body
2.16 Force Function for a Body and a Small Body
2.17 Force Function Expressions for the Moment Exerted
on a Body by a Particle
2.18 Force Function Expression for the Moment Exerted
on a Small Body by a Body
Chapter 3 Simple Spacecraft
3.1 Rotational Motion of a Torque-Free, Axisymmetric
Rigid Body
3.2 Effect of a Gravitational Moment on an Axisymmetric
Rigid Body in a Circular Orbit
3.3 Influence of Orbit Eccentricity on the Rotational Motion of
an Axisymmetric Rigid Body
3.4 Torque-Free Motion of an Unsymmetric Rigid Body
3.5 Effect of a Gravitational Moment on an Unsymmetric Rigid
Body in a Circular Orbit
3.6 Angular Momentum, Inertia Torque, and Kinetic Energy of
a Gyrostat
3.7 Dynamical Equations for a Simple Gyrostat
3.8 Rotational Motion of a Torque-Free, Axisymmetric Gyrostat
3.9 Reorientation of a Torque-Free Gyrostat Initially at Rest
3.10 Effect of a Gravitational Moment on an Axisymmetric
Gyrostat in a Circular Orbit
3.11 Effect of a Gravitational Moment on an Unsymmetric
Gyrostat in a Circular Orbit
Chapter 4 Complex Spacecraft
4.1 Generalized Active Forces
4.2 Potential Energy
4.3 Generalized Inertia Forces
4.4 Kinetic Energy
CONTENTS V
4.5 Dynamical Equations 275
4.6 Linearized Dynamical Equations 277
4.7 Computerization of Symbol Manipulation 279
4.8 Discrete Multi-Degree-of-Freedom Systems 284
4.9 Lumped Mass Models of Spacecraft 296
4.10 Spacecraft with Continuous Elastic Components 318
4.11 Use of the Finite Element Method for the Construction of
Modal Functions 332
Problem Sets 344
Problem Set 1 344
Problem Set 2 358
Problem Set 3 378
Problem Set 4 395
Appendixes 422
I Direction Cosines as Functions of Orientation Angles 422
II Kinematical Differential Equations in Terms
Orientation Angles 427
Index 433