Dedication
Preface
Supplements to the text
Acknowledgements
Chapter 1. Dynamics of Point Masses
Abstract
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
Problems
Section 1.3
Section 1.4
Section 1.5
Section 1.6
Section 1.7
Section 1.8
Chapter 2. The Two-Body Problem
Abstract
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
Problems
Section 2.2
Section 2.3
Section 2.4
Section 2.5
Section 2.6
Section 2.7
Section 2.8
Section 2.9
Section 2.11
Section 2.12
Chapter 3. Orbital Position as a Function of Time
Abstract
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
Section 3.4
Section 3.5
Section 3.6
Section 3.7
Chapter 4. Orbits in Three Dimensions
Abstract
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
Section 4.4
Section 4.5
Section 4.6
Section 4.7
Section 4.8
Chapter 5. Preliminary Orbit Determination
Abstract
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
Section 5.3
Section 5.4
Section 5.8
Section 5.10
Chapter 6. Orbital Maneuvers
Abstract
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
Section 6.3
Section 6.4
Section 6.5
Section 6.6
Section 6.7
Section 6.8
Section 6.9
Section 6.10
Chapter 7. Relative Motion and Rendezvous
Abstract
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
Section 7.3
Section 7.4
Section 7.5
Section 7.6
Chapter 8. Interplanetary Trajectories
Abstract
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
Section 8.3
Section 8.4
Section 8.6
Section 8.7
Section 8.8
Section 8.9
Section 8.10
Section 8.11
Chapter 9. Rigid Body Dynamics
Abstract
9.1 Introduction
9.2 Kinematics
9.3 Equations of translational motion
9.4 Equations of rotational motion
9.5 Moments of inertia
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
Section 9.5
Section 9.7
Section 9.8
Section 9.9
Chapter 10. Satellite Attitude Dynamics
Abstract
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
10.9 Gyroscopic attitude control
10.10 Gravity-gradient stabilization
Problems
Section 10.3
Section 10.4
Section 10.6
Section 10.7
Section 10.8
Section 10.9
Section 10.10
Chapter 11. Rocket Vehicle Dynamics
Abstract
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
Problems
Section 11.5
Section 11.6
Chapter 12. Introduction to Orbital Perturbations
Abstract
12.1 Introduction
12.2 Cowell’s method
12.3 Encke’s method
12.4 Atmospheric drag
12.5 Gravitational perturbations
12.6 Variation of parameters
12.7 Gauss variational equations
12.8 Method of averaging
12.9 Solar radiation pressure
12.10 Lunar gravity
12.11 Solar gravity
Problems
Section 12.3
Section 12.4
Section 12.5
Section 12.6
Section 12.7
Section 12.8
Section 12.9
Section 12.10
Section 12.11
Appendix A. Physical Data
Appendix B. A Road Map
Appendix C. Numerical Integration of the n-Body Equations of Motion
Appendix E. Gravitational Potential of a Sphere
Appendix F. Computing the Difference Between Nearly Equal Numbers
References and Further Reading
Index
Appendix D. MATLAB Scripts
D.1 Introduction
Chapter 1
D.3 Algorithm 1.2: Numerical integration by Heun’s predictor-corrector method
Chapter 2
D.6 Algorithm 2.2: Numerical solution of the two-body relative motion problem
D.7 Calculation of the Lagrange f and g functions and their time derivatives in terms of change in true anomaly
D.8 Algorithm 2.3: Calculate the state vector from the initial state vector and the change in true anomaly
D.9 Algorithm 2.4: Find the root of a function using the bisection method
D.10 MATLAB solution of Example 2.18
Chapter 3
D.12 Algorithm 3.2: Solution of Kepler’s equation for the hyperbola using Newton’s method
D.13 Calculation of the Stumpff functions S(z) and C(z)
D.14 Algorithm 3.3: Solution of the universal Kepler’s equation using Newton’s method
D.15 Calculation of the Lagrange coefficients f and g and their time derivatives in terms of change in universal anomaly
D.16 Algorithm 3.4: Calculation of the state vector given the initial state vector and the time lapse Δt
Chapter 4
D.18 Algorithm 4.2: Calculation of the orbital elements from the state vector
D.19 Calculation of tan–1 (y/x) to lie in the range 0 to 360°
D.20 Algorithm 4.3: Obtain the classical Euler angle sequence from a direction cosine matrix
D.21 Algorithm 4.4: Obtain the yaw, pitch, and roll angles from a direction cosine matrix
D.22 Algorithm 4.5: Calculation of the state vector from the orbital elements
D.23 Algorithm 4.6 Calculate the ground track of a satellite from its orbital elements
Chapter 5
D.25 Algorithm 5.2: Solution of Lambert’s problem
D.26 Calculation of Julian day number at 0 hr UT
D.27 Algorithm 5.3: Calculation of local sidereal time
D.28 Algorithm 5.4: Calculation of the state vector from measurements of range, angular position, and their rates
D.29 Algorithms 5.5 and 5.6: Gauss method of preliminary orbit determination with iterative improvement
Chapter 6
Chapter 7
D.32 Plot the position of one spacecraft relative to another
D.33 Solution of the linearized equations of relative motion with an elliptical reference orbit
Chapter 8
D.35 Algorithm 8.1: Calculation of the heliocentric state vector of a planet at a given epoch
D.36 Algorithm 8.2: Calculation of the spacecraft trajectory from planet 1 to planet 2
Chapter 9
D.38 Algorithm 9.2: Calculate the quaternion from the direction cosine matrix
D.39 Example 9.23: Solution of the spinning top problem
Chapter 11
Chapter 12
D.43 J2 perturbation of an orbit using Encke’s method
D.44 Example 12.6: Using Gauss variational equations to assess J2 effect on orbital elements
D.45 Algorithm 12.2: Calculate the geocentric position of the sun at a given epoch
D.46 Algorithm 12.3: Determine whether or not a satellite is in earth’s shadow
D.47 Example 12.9: Use the Gauss variational equations to determine the effect of solar radiation pressure on an earth satellite’s orbital parameters
D.48 Algorithm 12.4: Calculate the geocentric position of the moon at a given epoch
D.49 Example 12.11: Use the Gauss variational equations to determine the effect of lunar gravity on an earth satellite’s orbital parameters
D.50 Example 12.12: Use the Gauss variational equations to determine the effect of solar gravity on an earth satellite’s orbital parameters
