Foundations of Space Dynamics 1st Edition by Ashish Tewari ISBN 1119455349 9781119455349

1. Introduction

• 1.1 Space Flight
  • 1.1.1 Atmosphere as Perturbing Environment
  • 1.1.2 Gravity as the Governing Force
  • 1.1.3 Topics in Space Dynamics
• 1.2 Reference Frames and Time Scales
  • 1.2.1 Sidereal Frame
  • 1.2.2 Celestial Frame
  • 1.2.3 Synodic Frame
  • 1.2.4 Julian Date
• 1.3 Classification of Space Missions
• Exercises
• References

2. Dynamics

• 2.1 Notation and Basics
• 2.2 Plane Kinematics
• 2.3 Newton’s Laws
• 2.4 Particle Dynamics
• 2.5 The n-Body Problem
• 2.6 Dynamics of a Body
• 2.7 Gravity Field of a Body
  • 2.7.1 Legendre Polynomials
  • 2.7.2 Spherical Coordinates
  • 2.7.3 Axisymmetric Body
  • 2.7.4 Spherical Body with Radially Symmetric Mass Distribution
• Exercises
• References

3. Keplerian Motion

• 3.1 The Two-Body Problem
• 3.2 Orbital Angular Momentum
• 3.3 Orbital Energy Integral
• 3.4 Orbital Eccentricity
• 3.5 Orbit Equation
  • 3.5.1 Elliptic Orbit
  • 3.5.2 Parabolic Orbit
  • 3.5.3 Hyperbolic Orbit
  • 3.5.4 Rectilinear Motion
• 3.6 Orbital Velocity and Flight Path Angle
• 3.7 Perifocal Frame and Lagrange’s Coefficients
• Exercises

4. Time in Orbit

• 4.1 Position and Velocity in an Elliptic Orbit
• 4.2 Solution to Kepler’s Equation
  • 4.2.1 Newton’s Method
  • 4.2.2 Solution by Bessel Functions
• 4.3 Position and Velocity in a Hyperbolic Orbit
• 4.4 Position and Velocity in a Parabolic Orbit
• 4.5 Universal Variable for Keplerian Motion
• Exercises
• References

5. Orbital Plane

• 5.1 Rotation Matrix
• 5.2 Euler Axis and Principal Angle
• 5.3 Elementary Rotations and Euler Angles
• 5.4 Euler-Angle Representation of the Orbital Plane
  • 5.4.1 Celestial Reference Frame
  • 5.4.2 Local-Horizon Frame
  • 5.4.3 Classical Euler Angles
• 5.5 Planet-Fixed Coordinate System
• Exercises

6. Orbital Manoeuvres

• 6.1 Single-Impulse Orbital Manoeuvres
• 6.2 Multi-impulse Orbital Transfer
  • 6.2.1 Hohmann Transfer
  • 6.2.2 Rendezvous in Circular Orbit
  • 6.2.3 Outer Bi-elliptic Transfer
• 6.3 Continuous Thrust Manoeuvres
  • 6.3.1 Planar Manoeuvres
  • 6.3.2 Constant Radial Acceleration from Circular Orbit
  • 6.3.3 Constant Circumferential Acceleration from Circular Orbit
  • 6.3.4 Constant Tangential Acceleration from Circular Orbit
• Exercises
• References

7. Relative Motion in Orbit

• 7.1 Hill-Clohessy-Wiltshire Equations
• 7.2 Linear State-Space Model
• 7.3 Impulsive Manoeuvres About a Circular Orbit
  • 7.3.1 Orbital Rendezvous
• 7.4 Keplerian Relative Motion
• Exercises

8. Lambert’s Problem

• 8.1 Two-Point Orbital Transfer
  • 8.1.1 Transfer Triangle and Terminal Velocity Vectors
• 8.2 Elliptic Transfer
  • 8.2.1 Locus of the Vacant Focii
  • 8.2.2 Minimum-Energy and Minimum-Eccentricity Transfers
• 8.3 Lambert’s Theorem
  • 8.3.1 Time in Elliptic Transfer
  • 8.3.2 Time in Hyperbolic Transfer
  • 8.3.3 Time in Parabolic Transfer
• 8.4 Solution to Lambert’s Problem
  • 8.4.1 Parameter of Transfer Orbit
  • 8.4.2 Stumpff Function Method
  • 8.4.3 Hypergeometric Function Method
• Exercises
• References

9. Orbital Perturbations

• 9.1 Perturbing Acceleration
• 9.2 Osculating Orbit
• 9.3 Variation of Parameters
  • 9.3.1 Lagrange Brackets
• 9.4 Lagrange Planetary Equations
• 9.5 Gauss Variational Model
• 9.6 Variation of Vectors
• 9.7 Mean Orbital Perturbation
• 9.8 Orbital Perturbation Due to Oblateness
  • 9.8.1 Sun-Synchronous Orbits
  • 9.8.2 Molniya Orbits
• 9.9 Effects of Atmospheric Drag
  • 9.9.1 Life of a Satellite in a Low Circular Orbit
  • 9.9.2 Effect on Orbital Angular Momentum
  • 9.9.3 Effect on Orbital Eccentricity and Periapsis
• 9.10 Third-Body Perturbation
  • 9.10.1 Lunar and Solar Perturbations on an Earth Satellite
  • 9.10.2 Sphere of Influence and Conic Patching
• 9.11 Numerical Methods for Perturbed Keplerian Motion
  • 9.11.1 Cowell’s Method
  • 9.11.2 Encke’s Method
• Exercises
• References

10. Three-Body Problem

• 10.1 Equations of Motion
• 10.2 Particular Solutions by Lagrange
  • Equilibrium Solutions in a Rotating Frame
  • Conic Section Solutions
• 10.3 Circular Restricted Three-Body Problem
  • 10.3.1 Equations of Motion in the Inertial Frame
• 10.4 Non-dimensional Equations in the Synodic Frame
• 10.5 Lagrangian Points and Stability
  • 10.5.1 Stability Analysis
• 10.6 Orbital Energy and Jacobi’s Integral
  • 10.6.1 Zero-Relative-Speed Contours
  • 10.6.2 Tisserand’s Criterion
• 10.7 Canonical Formulation
• 10.8 Special Three-Body Trajectories
  • 10.8.1 Perturbed Orbits About a Primary
  • 10.8.2 Free-Return Trajectories
• Exercises
• References

11. Attitude Dynamics

• 11.1 Euler’s Equations of Attitude Kinetics
• 11.2 Attitude Kinematics
• 11.3 Rotational Kinetic Energy
• 11.4 Principal Axes
• 11.5 Torque-Free Rotation of Spacecraft
  • 11.5.1 Stability of Rotational States
• 11.6 Precession and Nutation
• 11.7 Semi-Rigid Spacecraft
  • 11.7.1 Dual-Spin Stability
• 11.8 Solution to Torque-Free Euler’s Equations
  • 11.8.1 Axisymmetric Spacecraft
  • 11.8.2 Jacobian Elliptic Functions
  • 11.8.3 Range-Kutta Solution
• 11.9 Gravity-Gradient Stabilization
• Exercises

12. Attitude Manoeuvres

• 12.1 Impulsive Manoeuvres with Attitude Thrusters
  • 12.1.1 Single-Axis Rotation
  • 12.1.2 Rigid Axisymmetric Spin-Stabilized Spacecraft
  • 12.1.3 Spin-Stabilized Asymmetric Spacecraft
• 12.2 Attitude Manoeuvres with Rotors
  • 12.2.1 Reaction Wheel
  • 12.2.2 Control-Moment Gyro
  • 12.2.3 Variable-Speed Control-Moment Gyro