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An introduction to orbital mechanics and spacecraft attitude dynamics
Foundations of Space Dynamics offers an authoritative text that combines a comprehensive review of both orbital mechanics and dynamics. The author?a noted expert in the field?covers up-to-date topics including: orbital perturbations, Lambert's transfer, formation flying, and gravity-gradient stabilization. The text provides an introduction to space dynamics in its entirety, including important analytical derivations and practical space flight examples.
Written in an accessible and concise style, Foundations of Space Dynamics highlights analytical development and rigor, rather than numerical solutions via ready-made computer codes. To enhance learning, the book is filled with helpful tables, figures, exercises, and solved examples.
This important book:
* Covers space dynamics with a systematic and comprehensive approach
* Is designed to be a practical text filled with real-world examples
* Contains information on the most current applications
* Includes up-to-date topics from orbital perturbations to gravity- gradient stabilization
* Offers a deep understanding of space dynamics often lacking in other textbooks
Written for undergraduate and graduate students and professionals in aerospace engineering, Foundations of Space Dynamics offers an introduction to the most current information on orbital mechanics and dynamics.
List of contents
Preface xiii
1 Introduction 1
1.1 Space Flight 1
1.1.1 Atmosphere as Perturbing Environment 1
1.1.2 Gravity as the Governing Force 4
1.1.3 Topics in Space Dynamics 5
1.2 Reference Frames and Time Scales 5
1.2.1 Sidereal Frame 5
1.2.2 Celestial Frame 8
1.2.3 Synodic Frame 8
1.2.4 Julian Date 8
1.3 Classification of Space Missions 10
Exercises 10
References 11
2 Dynamics 13
2.1 Notation and Basics 13
2.2 Plane Kinematics 14
2.3 Newton's Laws 16
2.4 Particle Dynamics 17
2.5 The n-Body Problem 20
2.6 Dynamics of a Body 24
2.7 Gravity Field of a Body 27
2.7.1 Legendre Polynomials 29
2.7.2 Spherical Coordinates 31
2.7.3 Axisymmetric Body 34
2.7.4 Spherical Body with Radially Symmetric Mass Distribution 37
Exercises 37
References 40
3 Keplerian Motion 41
3.1 The Two-Body Problem 41
3.2 Orbital Angular Momentum 43
3.3 Orbital Energy Integral 45
3.4 Orbital Eccentricity 46
3.5 Orbit Equation 49
3.5.1 Elliptic Orbit 53
3.5.2 Parabolic Orbit 56
3.5.3 Hyperbolic Orbit 56
3.5.4 Rectilinear Motion 58
3.6 Orbital Velocity and Flight Path Angle 60
3.7 Perifocal Frame and Lagrange's Coefficients 63
Exercises 65
4 Time in Orbit 69
4.1 Position and Velocity in an Elliptic Orbit 70
4.2 Solution to Kepler's Equation 75
4.2.1 Newton's Method 76
4.2.2 Solution by Bessel Functions 78
4.3 Position and Velocity in a Hyperbolic Orbit 80
4.4 Position and Velocity in a Parabolic Orbit 84
4.5 Universal Variable for Keplerian Motion 86
Exercises 88
References 89
5 Orbital Plane 91
5.1 Rotation Matrix 91
5.2 Euler Axis and Principal Angle 94
5.3 Elementary Rotations and Euler Angles 97
5.4 Euler-Angle Representation of the Orbital Plane 101
5.4.1 Celestial Reference Frame 103
5.4.2 Local-Horizon Frame 104
5.4.3 Classical Euler Angles 106
5.5 Planet-Fixed Coordinate System 111
Exercises 114
6 Orbital Manoeuvres 117
6.1 Single-Impulse Orbital Manoeuvres 119
6.2 Multi-impulse Orbital Transfer 123
6.2.1 Hohmann Transfer 124
6.2.2 Rendezvous in Circular Orbit 127
6.2.3 Outer Bi-elliptic Transfer 130
6.3 Continuous Thrust Manoeuvres 133
6.3.1 Planar Manoeuvres 134
6.3.2 Constant Radial Acceleration from Circular Orbit 135
6.3.3 Constant Circumferential Acceleration from Circular Orbit 136
6.3.4 Constant Tangential Acceleration from Circular Orbit 139
Exercises 141
References 143
7 Relative Motion in Orbit 145
7.1 Hill-Clohessy-Wiltshire Equations 148
7.2 Linear State-Space Model 151
7.3 Impulsive Manoeuvres About a Circular Orbit 153
7.3.1 Orbital Rendezvous 153
7.4 Keplerian Relative Motion 155
Exercises 158
8 Lambert's Problem 161
8.1 Two-Point Orbital Transfer 161
8.1.1 Transfer Triangle and Terminal Velocity Vectors 162
8.2 Elliptic Transfer 164
8.2.1 Locus of the Vacant Focii 165
8.2.2 Minimum-Energy and Minimum-Eccentricity Transfers 166
8.3 Lambert's Theorem 168
8.3.1 Time in Elliptic Transfer 169
8.3.2 Time in Hyperbolic
About the author
Ashish Tewari is a Professor in the Department of Aerospace Engineering at IIT Kanpur. He specializes in flight mechanics and control.
