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Orbital Mechanics for Engineering Students.pdf
cover
title page
copyright page
contents
preface
acknowledgments
CHAPTER 1 Dynamics of point masses
1.1 Introduction
1.2 Vectors
1.3 Kinematics
1.4 Mass, force and Newton's law of gravitation
1.5 Newton's law of motion
1.6 Time derivatives of moving vectors
1.7 Relative motion
1.8 Numerical integration
1.8.1 Runge-Kutta methods
1.8.2 Heun's Predictor-Corrector method
1.8.3 Runge-Kutta with variable step size
Problems
List of Key Terms
CHAPTER 2 The two-body problem
2.1 Introduction
2.2 Equations of motion in an inertial frame
2.3 Equations of relative motion
2.4 Angular momentum and the orbit formulas
2.5 The energy law
2.6 Circular orbits (e = 0)
2.7 Elliptical orbits (0 < e < 1)
2.8 Parabolic trajectories (e = 1)
2.9 Hyperbolic trajectories (e > 1)
2.10 Perifocal frame
2.11 The lagrange coefficients
2.12 Restricted three-body problem
2.12.1 Lagrange points
2.12.2 Jacobi constant
Problems
List of Key Terms
CHAPTER 3 Orbital position as a function of time
3.1 Introduction
3.2 Time since periapsis
3.3 Circular orbits (e = 0)
3.4 Elliptical orbits (e < 1)
3.5 Parabolic trajectories (e = 1)
3.6 Hyperbolic trajectories (e < 1)
3.7 Universal variables
Problems
List of Key Terms
CHAPTER 4 Orbits in three dimensions
4.1 Introduction
4.2 Geocentric right ascension-declination frame
4.3 State vector and the geocentric equatorial frame
4.4 Orbital elements and the state vector
4.5 Coordinate transformation
4.6 Transformation between geocentric equatorial and perifocal frames
4.7 Effects of the Earth's oblateness
4.8 Ground tracks
Problems
List of Key Terms
CHAPTER 5 Preliminary orbit determination
5.1 Introduction
5.2 Gibbs method of orbit determination from three position vectors
5.3 Lambert's problem
5.4 Sidereal time
5.5 Topocentric coordinate system
5.6 Topocentric equatorial coordinate system
5.7 Topocentric horizon coordinate system
5.8 Orbit determination from angle and range measurements
5.9 Angles only preliminary orbit determination
5.10 Gauss method of preliminary orbit determination
Problems
List of Key Terms
CHAPTER 6 Orbital maneuvers
6.1 Introduction
6.2 Impulsive maneuvers
6.3 Hohmann transfer
6.4 Bi-elliptic Hohmann transfer
6.5 Phasing maneuvers
6.6 Non-Hohmann transfers with a common apse line
6.7 Apse line rotation
6.8 Chase maneuvers
6.9 Plane change maneuvers
6.10 Nonimpulsive orbital maneuvers
Problems
List of Key Terms
CHAPTER 7 Relative motion and rendezvous
7.1 Introduction
7.2 Relative motion in orbit
7.3 Linearization of the equations of relative motion in orbit
7.4 Clohessy-Wiltshire equations
7.5 Two-impulse rendezvous maneuvers
7.6 Relative motion in close-proximity circular orbits
Problems
List of Key Terms
CHAPTER 8 Interplanetary trajectories
8.1 Introduction
8.2 Interplanetary Hohmann transfers
8.3 Rendezvous Opportunities
8.4 Sphere of influence
8.5 Method of patched conics
8.6 Planetary departure
8.7 Sensitivity analysis
8.8 Planetary rendezvous
8.9 Planetary flyby
8.10 Planetary ephemeris
8.11 Non-Hohmann interplanetary trajectories
Problems
List of Key Terms
CHAPTER 9 Rigid-body dynamics
9.1 Introduction
9.2 Kinematics
9.3 Equations of translational motion
9.4 Equations of rotational motion
9.5 Moments of inertia
9.5.1 Parallel axis theorem
9.6 Euler's equations
9.7 Kinetic energy
9.8 The spinning top
9.9 Euler angles
9.10 Yaw, pitch and roll angles
9.11 Quaternions
Problems
List of Key Terms
CHAPTER 10 Satellite attitude dynamics
10.1 Introduction
10.2 Torque-free motion
10.3 Stability of torque-free motion
10.4 Dual-spin spacecraft
10.5 Nutation damper
10.6 Coning maneuver
10.7 Attitude control thrusters
10.8 Yo-yo despin mechanism
10.8.1 Radial release
10.9 Gyroscopic attitude control
10.10 Gravity gradient stabilization
Problems
List of Key Terms
CHAPTER 11 Rocket vehicle dynamics
11.1 Introduction
11.2 Equations of motion
11.3 The thrust equation
11.4 Rocket performance
11.5 Restricted staging in field-free space
11.6 Optimal staging
11.6.1 Lagrange multiplier
Problems
List of Key Terms
Appendix A Physical data
Appendix B A road map
Appendix C Numerical intergration of the n-body equations of motion
Appendix D MATLAB® algorithms
Appendix E Gravitational potential energy of a sphere
References
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
Orbital Mechanics for
Engineering Students
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Orbital Mechanics for
Engineering Students
Second Edition
Howard D. Curtis
Professor of Aerospace Engineering
Embry -Riddle Aeronautical University
Daytona Beach, Florida
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
CHAPTER 1 Dynamics of point masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Mass, force and Newton’s law of gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 Newton’s law of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Time derivatives of moving vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.7 Relative motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.8 Numerical integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.8.1 Runge-Kutta methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.8.2 Heun’s Predictor-Corrector method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
1.8.3 Runge-Kutta with variable step size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
List of Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
CHAPTER 2 The two-body problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.2 Equations of motion in an inertial frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.3 Equations of relative motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.4 Angular momentum and the orbit formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.5 The energy law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2.6 Circular orbits (e ⫽ 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.7 Elliptical orbits (0 < e < 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.8 Parabolic trajectories (e ⫽ 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.9 Hyperbolic trajectories (e > 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.10 Perifocal frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.11 The lagrange coeffi cients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
2.12 Restricted three-body problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
2.12.1 Lagrange points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
2.12.2 Jacobi constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
List of Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
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