Orbital Mechanics for Engineering Students

Orbital Mechanics for Engineering Students

3rd Edition - October 5, 2013

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  • Author: Howard Curtis
  • eBook ISBN: 9780080977485

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Written by Howard Curtis, Professor of Aerospace Engineering at Embry-Riddle University, Orbital Mechanics for Engineering Students is a crucial text for students of aerospace engineering. Now in its 3e, the book has been brought up-to-date with new topics, key terms, homework exercises, and fully worked examples. Highly illustrated and fully supported with downloadable MATLAB algorithms for project and practical work, this book provides all the tools needed to fully understand the subject.

Key Features

  • New chapter on orbital perturbations
  • New and revised examples and homework problems
  • Increased coverage of attitude dynamics, including new MATLAB algorithms and examples


Undergraduate students in aerospace, astronautical, mechanical engineering, and engineering physics; related professional aerospace and space engineering fields.

Table of Contents

  • Dedication


    Supplements to the text


    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


    Section 1.3

    Section 1.4

    Section 1.5

    Section 1.6

    Section 1.7

    Section 1.8

    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


    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


    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


    Section 3.4

    Section 3.5

    Section 3.6

    Section 3.7

    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


    Section 4.4

    Section 4.5

    Section 4.6

    Section 4.7

    Section 4.8

    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


    Section 5.3

    Section 5.4

    Section 5.8

    Section 5.10

    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


    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


    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


    Section 7.3

    Section 7.4

    Section 7.5

    Section 7.6

    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


    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


    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


    Section 9.5

    Section 9.7

    Section 9.8

    Section 9.9

    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

    10.9 Gyroscopic attitude control

    10.10 Gravity-gradient stabilization


    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


    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


    Section 11.5

    Section 11.6

    Chapter 12. Introduction to Orbital Perturbations


    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


    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


    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

Product details

  • No. of pages: 768
  • Language: English
  • Copyright: © Butterworth-Heinemann 2013
  • Published: October 5, 2013
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780080977485

About the Author

Howard Curtis

Professor Curtis is former professor and department chair of Aerospace Engineering at Embry-Riddle Aeronautical University. He is a licensed professional engineer and is the author of two textbooks (Orbital Mechanics 3e, Elsevier 2013, and Fundamentals of Aircraft Structural Analysis, McGraw Hill 1997). His research specialties include continuum mechanics, structures, dynamics, and orbital mechanics.

Affiliations and Expertise

Professor Emeritus, Aerospace Engineering, Embry-Riddle Aeronautical University, Florida, USA

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