Introduction to Space Dynamics

by William Tyrrell Thomson

Overview

Although this classic introduction to space-flight engineering was first published not long after Sputnik was launched, the fundamental principles it elucidates are as varied today as then. The problems to which these principles are applied have changed, and the widespread use of computers has accelerated problem-solving techniques, but this book is still a valuable basic text for advanced undergraduate and graduate students of aerospace engineering.
The first two chapters cover vector algebra and kinematics, including angular velocity vector, tangential and normal components, and the general case of space motion. The third chapter deals with the transformation of coordinates, with sections of Euler's angles, and the transformation of angular velocities.
A variety of interesting problems regarding the motion of satellites and other space vehicles is discussed in Chapter 4, which includes the two-body problem, orbital change due to impulsive thrust, long-range ballistic trajectories, and the effect of the Earth's oblateness. The fifth and sixth chapters describe gyrodynamics and the dynamics of gyroscopic instruments, covering such topics as the displacement of a rigid body, precession and nutation of the Earth's polar axis, oscillation of the gyrocompass, and inertial navigation.
Chapter 7 is an examination of space vehicle motion, with analyses of general equations in body conditions and their transformation to inertial coordinates, attitude drift of space vehicles, and variable mass. The eighth chapter discusses optimization of the performance of single-stage and multistage rockets. Chapter 9 deals with generalized theories of mechanics, including holonomic and non-holonomic systems, Lagrange's Equation for impulsive forces, and missile dynamics analysis.
Throughout this clear, comprehensive text, practice problems (with answers to many) aid the student in mastering analytic techniques, and numerous charts and diagrams reinforce each lesson. 1961 edition.

Product Details

ISBN-13:	9780486651132
Publisher:	Dover Publications
Publication date:	06/01/1986
Series:	Dover Books on Aeronautical Engineering
Edition description:	Unabridged
Pages:	352
Sales rank:	719,691
Product dimensions:	5.50(w) x 8.50(h) x (d)

Table of Contents

Chapter 1. Introduction
1.1 Basic concepts
1.2 Scalar and Vector Quantities
1.3 Properties of a Vector
1.4 Moment of a Vector
1.5 Angular Velocity Vector
1.6 Derivative of a Vector
Chapter 2. Kinematics
2.1 Velocity and acceleration
2.2 Plane Motion (Radial and Transverse Components)
2.3 Tangential and Normal Components
2.4 Plane Motion along a Rotating Curve (Relative Motion)
2.5 General Case of Space Motion
2.6 Motion Relative to the Rotating Earth
Chapter 3. Transformation of Coordinates
3.1 Transformation of Displacements
3.2 Transformation of Velocites
3.3 Instantaneous Center
3.4 Euler's Angles
3.5 Transformation of Angular Velocities
Chapter 4. Particle Dynamics (Satellite Orbits)
4.1 Force and Momentum
4.2 Impulse and Momentum
4.3 Work and Energy
4.4 Moment of Momentum
4.5 Motion Under a Central Force
4.6 The Two-body Problem
4.7 Orbits of Planets and Satellites
4.8 Geometry of conic Sections
4.9 Orbit Established from Initial conditions
4.10 Satellite Launched with beta subscript 0 = 0
4.11 Cotangential Transfer between Coplanar Circular Orbits
4.12 Transfer between Coplanar Coaxial Elliptic Orbits
4.13 Orbital Change due to Impulsive Thrust
4.14 Perturbation of Orbital Parameters
4.15 Stability of Small Oscillations about a Circular Orbit
4.16 Interception and Rendezvous
4.17 Long-Range Ballistic Trajectories
4.18 Effect of the Earth's Oblateness
Chapter 5. Gyrodynamics
5.1 Displacement of a Rigid Body
5.2 Moment of Momentum of a Rigid Body (About a Fixed Point or the Moving Center of Mass)
5.3 Kinetic Energy of a Rigid Body
5.4 Moment of Inertia about a Rotated Axis
5.5 Principal Axes
5.6 Euler's Moment Equation
5.7 Euler's Equation for Principal Axes
5.8 Body of Revolution with Zero External Moment (Body Coordinates)
5.9 Body of Revolution with Zero Moment, in Terms of Euler's Angles
5.10 Unsymmetrical Body with Zero External Moment (Poinsot's Geometric Solution)
5.11 Unequal Moments of Inertia with Zero Moment (Analytical Solution)
5.12 Stability of Rotation about Principal Axes
5.13 General Motion of a Symmetric Gyro or Top
5.14 Steady Precession of a Symmetric Gyro or Top
5.15. Precession and Nutation of the Earth's Polar Axis
5.16 General Motion of a Rigid Body
Chapter 6. Dynamics of Gyroscopic Instruments
6.1 Small Oscillations of Gyros
6.2 Oscilaltions About Gimbal Axes
6.3 Gimbal Masses Included (Perturbation Technique)
6.4 The Gyrocompass
6.5 Oscillation of the Gyrocompass
6.6 The Rate Gyro
6.7 The Integrating Gyro
6.8 The Stable Platform
6.9 The Three-Axis Platform
6.10 Inertial Navigation
6.11 Oscillation of Navigational Errors
Chapter 7. Space Vehicle Motion
7.1 General Equations in Body Coordinates
7.2 Thrust Misalignment
7.3 Rotations Referred to Inertial Coordinates
7.4 Near Symmetric Body of Revolution with Zero Moment
7.5 Despinning of Satellites
7.6 Attitude Drift of Space Vehicles
7.7 Variable Mass
7.8 Jet Damping (Nonspinning Variable Mass Rocket)
7.9 Euler's Dynamical Equations for Spinning Rockets
7.10 Angle of Attack of the Missile
7.11 General Motion of Spinning Bodies with Varying Configuration and Mass
Chapter 8. Performance and Optimization
8.1 Performance of Single-Stage Rockets
8.2 Optimization of Multistage Rockets
8.3 Flight Trajectory Optimization
8.4 Optimum Program for Propellant Utilization
8.5 Gravity Turn
Chapter 9. Generalized Theories of Mechanics
9.1 Introduction
9.2 System with Constraints
9.3 Generalized Coordinates
9.4 Holonomic and Nonholonomic systems
9.5 Principle of Virtual work
9.6 D'Alembert's Principle
9.7 Hamilton's Principle
9.8 Lagrange's Equation (Holonomic system)
9.9 Nonholonomic System
9.10 Lagrange's Equation for Impulsive Forces
9.11 Lagrange's Equations for Rotating Coordinates
9.12 Missile Dynamic Analysis
General References
Appendix A. Matrices
Appendix B. Dyadics
Appendix C. The Variational Calculus
Index