Space Vehicle Maneuvering, Propulsion, Dynamics and Control: A Textbook for Engineers

Preface
Contents
List of Abbreviations
Chapter 1: Celestial Mechanics: Keplerian Orbits
	1.1 Introduction: The Space Environment
		1.1.1 Density Behaviour in the Exosphere (Hydrostatic Model)
		1.1.2 Key Features of the Intervening Environment Between the Earth and the Sun
		1.1.3 Environmental Effects to Spacecraft
		1.1.4 The Thermal Environment and Thermal Control
		1.1.5 Space Debris
		1.1.6 The Launch Environment
	1.2 Orbital Motion: The Two-Body Problem and Kepler´s Laws
		1.2.1 Elliptic, Parabolic and Hyperbolic Orbits
		1.2.2 Newton´s Law of Gravitation
		1.2.3 Keplerian Model, Orbital Elements
		1.2.4 Definition of a Keplerian Orbit
	1.3 Energy Considerations: The Vis-Viva Equation
		1.3.1 Escape Velocity, Circular Velocity
		1.3.2 Hyperbolic Orbits: The Turning Angle and the Excess Velocity
		1.3.3 Application to Gravity Assist
		1.3.4 Lambert´s Problem and Its Solution
	1.4 Relative Motion Equations: Hill-Clohessy-Wiltshire Equations
	1.5 Real Orbits, the Three-Body Problem
		1.5.1 The Equilibrium Points
		1.5.2 Stability of the Lagrange Points
		1.5.3 Application of the CR3BP and the Lagrange Points
	Exercises
	References
Chapter 2: Celestial Mechanics: Real Orbits
	2.1 Real Orbits: Perturbations
	2.2 Gauss Perturbation Equations
		2.2.1 Nonsingular Orbital Elements
		2.2.2 Gravitational Perturbations, Station Keeping
		2.2.3 Non-spherical Nature of Central Body-1
		2.2.4 Oblateness (J2) Perturbations
		2.2.5 Orbital Averaging, Precession of the Line of Apsides, Regression of the Line of Nodes, Secular J2 Perturbations
		2.2.6 Stability of a Spacecraft in a Geostationary Orbit: Station Keeping
		2.2.7 Third-Body Perturbations-2
		2.2.8 Third-Body Effects of the Moon and the Sun (Lunisolar)
	2.3 Non-gravitational Perturbations
		2.3.1 Aerodynamic Drag-3
		2.3.2 Prediction of the Drag Coefficient
	2.4 Solar Radiation Pressure and Wind
		2.4.1 Photonic Pressure-4
		2.4.2 Infrared Radiation + Albedo + Solar Wind-5, 6
	2.5 Magnetic Forces-7, Meteors and Space Debris Impact-8
	2.6 Control Forces-9
	Exercises
	References
Chapter 3: Space Vehicle Manoeuvring
	3.1 Principles of Space Vehicle Manoeuvring: Impulse Momentum-Basic Problem
	3.2 Estimating Δv Requirements for Orbit Changes
		3.2.1 Velocity Components, Law of Cosines, Law of Sines
		3.2.2 Orbit Plane Inclination Change
		3.2.3 Multiple Orbital Element Change
	3.3 Rotating the Line of Apsides
		3.3.1 Other Simple Keplerian Orbit Manoeuvres
		3.3.2 Circular to Elliptic and Vice Versa, Raising Apoapsis or Periapsis
	3.4 Two-Impulse Manoeuvres (Hohmann Transfer), Examples
		3.4.1 Hohmann Transfer: Coplanar Elliptic Transfer
		3.4.2 Examples of Coplanar Elliptic Hohmann Transfers
		3.4.3 Hohmann Transfer: Noncoplanar Elliptic Transfers
	3.5 Oberth´s and Edelbaum´s Multi-Impulse Manoeuvres
	3.6 Application of Lambert´s Problem to Space Vehicle Manoeuvring
	Exercises
	References
Chapter 4: Interplanetary Trajectories
	4.1 Interplanetary Trajectories
	4.2 Sphere of Influence (SOI)
	4.3 Patched Conic Method
		4.3.1 Interplanetary Trajectories
		4.3.2 Interplanetary Trajectories-Heliocentric Orbit Phase
		4.3.3 Planetary Escape, Planetary Approach and Re-entry
		4.3.4 Phasing and Launch Timing
	4.4 Application Examples, Moon, Mars (Or Other Outer Planet, E.G. Jupiter), Venus (Inner Planet)
		4.4.1 Lunar Trajectory
		4.4.2 Trajectory Design to an Outer Planet: Mars
		4.4.3 Trajectory Design to an Inner Planet: Venus
	Exercises
	References
Untitled
Chapter 5: Space Vehicle Mission Planning
	5.1 Mission Planning and Space Propulsion Systems
	5.2 Classification of Space Propulsion Systems
		5.2.1 Fundamental Concepts and Metrics
	5.3 Launch Vehicles
		5.3.1 Secondary Propulsion Systems (Chemical and Electric)
	5.4 Rocket Equation, Thrust and Specific Impulse
	5.5 Staging
		5.5.1 Multistaging: Maximizing Δv
		5.5.2 Application Example: Three Stage Rocket
	5.6 Maximizing Range, With Drag and Gravity Loss in the Boost Phase
	5.7 Electric Propulsion, Maximizing Δv, Payload Mass Ratio
		5.7.1 Application to Mission Design
	5.8 Chemical Propulsion
		5.8.1 Chemical Propulsion Systems
	Exercises
	References
Chapter 6: Trajectory Optimization and Feedback Control
	6.1 Trajectory Optimization Principles: Introduction
	6.2 Calculus of Variations and Pontryagin´s Minimum Principle
		6.2.1 Functionals, Variations and Pontryagin´s Minimum Principle
		6.2.2 Application to the Optimum Control Problem
		6.2.3 Boundary Conditions
		6.2.4 Example 1
		6.2.5 Transversality Conditions
		6.2.6 Example 2
	6.3 Optimal Tracking Trajectory Synthesis
		6.3.1 Application to Spacecraft Absolute Motion
		6.3.2 Application to Spacecraft Relative Motion
		6.3.3 Application to Spacecraft Motion in Spherical Coordinates
		6.3.4 Application to Spacecraft Motion in a CR3BP Setting
		6.3.5 Linear Optimal and Tracking Feedback Control
	6.4 Continuous Trajectory Correction Manoeuvres Using Feedback
	6.5 Control Laws Due to Edelbaum, Petropolous and Others
		6.5.1 Modifications of the Q Law
		6.5.2 Other Methods
	Exercises
	Appendix 6.1: Solving the Two-Point Boundary Value Problem for the Optimal Trajectory
	References
Chapter 7: Patched Three-Body Approximation: Application to Interplanetary Trajectory Planning
	7.1 Three-Body Problem
	7.2 Key Features of the Circular Restricted Three-Body Problem
		7.2.1 Altering the Coordinate System
		7.2.2 The Equilibrium or Lagrange Points
		7.2.3 The Hill Sphere and the Sphere of Influence
		7.2.4 Jacobi´s Integral and Constant
		7.2.5 HALO and Periodic Orbits: Stability and Linearization
		7.2.6 Linearization About Co-linear Libration Points
	7.3 Transformation of Synodic Reference Frames
		7.3.1 Example 1: Earth-Moon (μ = 0.01215), Sun-Earth (μ = 3.036e - 06) and Satellite Systems
		7.3.2 Example 2: Sun-Earth (μ = 3.036e - 06), Sun-Jupiter (μ = 9.5364e - 04) and Satellite Systems
	7.4 Methods for Generating Orbit Families
		7.4.1 Plotting the Manifolds and Trajectories
	7.5 The Bi-circular Restricted Four-Body Problem
		7.5.1 Motion of the Spacecraft in a Multi-body Environment
	7.6 The Patched Three-Body Approximation
		7.6.1 Example 1: Earth-Moon Transfer
		7.6.2 Example 2: Earth-Jupiter Transfer
	7.7 The Circular Restricted Three-body Problem with Applied Control Forces
		7.7.1 Planar Circular Restricted Three-Body Problem
		7.7.2 Multi-body Problems with Applied Forces and Continuous Thrust
	7.8 Optimal Steering Control Law for Orbit Raising
		7.8.1 Optimal Transfer with Constrained Orbit Raising
	7.9 Application Examples: Orbit Raising with Continuous Thrust
		7.9.1 Earth-Moon Transfer with Continuous Thrust
		7.9.2 Interplanetary Transfer with Continuous Thrust
		7.9.3 Discussion of the Application Example Results
	Exercises
	References
Chapter 8: Missions to the Asteroids
	8.1 Introduction
	8.2 Gravitational Potentials and Potential Modelling
		8.2.1 Spherical Harmonic Model
		8.2.2 MacCullagh´s Moment of Inertia-Based Formula
		8.2.3 Moment of Inertia Modelling
		8.2.4 Gravitational Potential Models
		8.2.5 Geoid Models
		8.2.6 Geometrical Modelling
		8.2.7 Polyhedron Model
		8.2.8 Discrete Element Models
		8.2.9 The MASCON Model
		8.2.10 Other Models
	8.3 Asteroid Equations of Motion
		8.3.1 Two-Body Problem: Equations of Motion
		8.3.2 Planar Equations of Motion
		8.3.3 Cartesian Coordinates
		8.3.4 Conditions of Equilibrium
		8.3.5 Stability of Equilibrium
	8.4 Asteroid Trajectories: Application Examples
	8.5 Three-Body Problem: Vector Equations of Motion in Rotating Coordinates with a Point Mass Model
		8.5.1 Three-Body Problem: Derivation of the Equations of Motion with a Finite Second Body
		8.5.2 Equations of Circular Restricted Motion in Rotating Coordinates
		8.5.3 Conditions of Equilibrium of the Circular Restricted Motion in Rotating Coordinates
		8.5.4 Stability of the Equilibrium Solutions
	8.6 Application to a Spacecraft Orbiting the Sun in the Vicinity of an Asteroid
		8.6.1 Solar Radiation Pressure (Based on a Flat Plate Model)
		8.6.2 Gravitational Potential with an Asteroid Present
	8.7 Asteroid Trajectory Examples
		8.7.1 De-tumbling Control of an Asteroid: Yo-Yo De-spin
		8.7.2 Asteroid Deflection
		8.7.3 Co-orbital Dynamics of Two Spacecraft
	Exercises
	References
Chapter 9: Physics of Plasmas
	9.1 Plasma and Physical Laws
	9.2 Electrostatics of Plasma
		9.2.1 Quasi-neutrality of the Plasma
		9.2.2 Plasma Oscillations
		9.2.3 Saha Ionization Equation
	9.3 The Hall Effect or the Hall Voltage
	9.4 Force Density on an Ion Stream in an Axial Electric Field: Magnitude of the Force Density
	9.5 Probabilistic Nature of Plasma Velocities: Plasma Velocities in an Electric Potential
		9.5.1 Average Kinetic Energy and Velocities
		9.5.2 Collisions Between Charged Particles and Debye Shielding
		9.5.3 Collective Behaviour of Plasma Particles
	9.6 Motion of a Single Charged Particle in an EM Field
		9.6.1 With an Applied Electric Field and General Motion
	9.7 Plasma Instability, Drifts due to Non-uniform Magnetic Fields and Curvature
		9.7.1 Axially Varying Magnetic Fields, Radial Component of the Magnetic Field and Components of the Lorentz Force
		9.7.2 Magnetic Mirrors and Plasma Confinement
		9.7.3 Non-uniform Electric Fields, Drift Instabilities and Time-Varying Fields
		9.7.4 Guiding Centre Drifts: Summary
	9.8 Plasma as a Fluid: Plasma Modelling and Electromagnetic Fields
		9.8.1 Maxwell´s Equations and the Complete Equations of Fluid Flow
		9.8.2 The Magneto-Gas Dynamic Equations, Equations of Charge-Neutral Fluid Flow in Vector Form
		9.8.3 Single Fluid Model: The MHD Equations
	9.9 Kinetic Theory of Plasma
		9.9.1 The Complete Set of MHD Equations
		9.9.2 Two Species Model: Maxwell´s Equations
	9.10 The Boltzmann and Vlasov Equation: Electron Distributions
	9.11 Mobility and Diffusion: Ambi-polar Diffusion and Plasma Decay
		9.11.1 Bohm Diffusion, Momentum Gain and Plasma Resistivity
	9.12 Quasi-one-dimensional Model and Transformation of Variables
	9.13 Applications
	Exercises
	References
Chapter 10: Space Vehicle Electric Propulsion
	10.1 Introduction to Electric Propulsion
	10.2 Electric Propulsion (EP) Basics and Schematics
		10.2.1 Electric Propulsion Performance
		10.2.2 Electric Propulsion Types and Overviews
		10.2.3 Physics of Electric Propulsion
	10.3 Electro-thermal Propulsion: Concepts
		10.3.1 Resistojets
		10.3.2 Arcjet Principles
		10.3.3 Emissions and Reactions in a Plasma Region
		10.3.4 Estimating the Current Density in a Plasma Region
		10.3.5 Microwave Jet Thrusters
	Exercises
	Appendix 10.1
		Basic Units Used in Plasma Physics
	Appendix 10.2
		List of Manufacturers and Some Useful Websites
			Chemical Propulsion Systems Manufacturers
			Electric Propulsion Systems Manufacturers
			Space Systems Manufacturers
			Academic Institutions (Universities) Involved in Space Research
	References
Chapter 11: Space Vehicle Electro-static and Electro-magnetic Propulsion
	11.1 Introduction
	11.2 Plasma Behaviour in Electric and Magnetic Fields
		11.2.1 Electro-static/Electro-magnetic Acceleration
		11.2.2 Generation of a Plasma at a Source
		11.2.3 Child-Langmuir Law
		11.2.4 Electro-static/Electro-magnetic Thrust Generation
	11.3 Typical Plasma Thrusters
		11.3.1 Gridded Ion Engines
		11.3.2 Pulsed Plasma Thrusters
		11.3.3 Hall Current Thrusters
		11.3.4 Field Effect Electric, Colloid Propulsion and Electrospray Thrusters
		11.3.5 The Physics of Cone and Droplet Formation
	Exercises
	Appendix 11.1: Useful Atomic Constants
	References
Chapter 12: Space Vehicle Electro-dynamic Propulsion
	12.1 Electro-dynamic Thrusters
	12.2 Role of a Magnetic Field in Plasma Acceleration
		12.2.1 Plasma Creation and Acceleration
		12.2.2 Plasma Magnetic Nozzles, Focussing and Magnetic Mirrors
	12.3 Electric Propulsion: Electrodeless and Gridless Systems
	12.4 Electromagnetic Plasma Thruster Families
		12.4.1 Magnetoplasmadynamic (MPD) Thrusters
		12.4.2 Self-Induced and Applied Field MPDTs
		12.4.3 Air-Breathing Electric Propulsion
	12.5 Pulsed Plasma Thruster
		12.5.1 Air-Breathing PPTs
	12.6 RF Excited Plasma Thrusters: Helicon Waves
		12.6.1 Analysis of Helicon Waves
		12.6.2 Eigenmodes of Helicon Waves
		12.6.3 General Dispersion Relations
		12.6.4 The Case of Cold Plasma
		12.6.5 Application to Magnetized Plasma with Two Species
		12.6.6 The Case of Helicon Waves
		12.6.7 Thrust from Plasma Exhaust
		12.6.8 Antennas for Helicon Waves
		12.6.9 Helicon Thruster Power Circuit
	12.7 Helicon Plasma Thrusters
		12.7.1 Helicon Plasma Thrusters: Design
	12.8 Variable Specific Impulse Magnetoplasma Rocket (VASIMR)
	12.9 Inertial Electrostatic Confinement (IEC) Thruster
	12.10 Summary of HPT Thrusters
	Exercises
	References
Index