Perturbing Acceleration
9.2 Osculating Orbit
9.3 Variation of Parameters
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
9.9 Effects of Atmospheric Drag
9.10 Third‐Body Perturbation
9.11 Numerical Methods for Perturbed Keplerian Motion
Exercises
References
16 10 Three‐Body Problem 10.1 Equations of Motion 10.2 Particular Solutions by Lagrange 10.3 Circular Restricted Three‐Body Problem 10.4 Non‐dimensional Equations in the Synodic Frame 10.5 Lagrangian Points and Stability 10.6 Orbital Energy and Jacobi's Integral 10.7 Canonical Formulation 10.8 Special Three‐Body Trajectories Exercises Reference
17 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 11.6 Precession and Nutation 11.7 Semi‐Rigid Spacecraft 11.8 Solution to Torque‐Free Euler's Equations 11.9 Gravity‐Gradient Stabilization Exercises
18 12 Attitude Manoeuvres 12.1 Impulsive Manoeuvres with Attitude Thrusters 12.2 Attitude Manoeuvres with Rotors Exercises References
19 ANumerical Solution of Ordinary Differential Equations A.1 Fixed‐Step Runge‐Kutta Algorithms A.2 Variable‐Step Runge‐Kutta Algorithms A.3 Runge‐Kutta‐Nyström Algorithms References
20 BJacobian Elliptic Functions Reference
21 Index
List of Tables
1 Chapter 1Table 1.1 Variation of density with altitude in Earth's atmosphere
2 Chapter 3Table 3.1 Two‐body orbits.
3 Chapter 4Table 4.1 Iteration steps for the solution of Kepler's equation by Newton's m...Table 4.2 Bessel functions of the first kind and order
4 Chapter 6Table 6.1 The specific impulse,
5 Chapter 7Table 7.1 Comparison of relative position and velocity in a geosynchronous or...
6 Chapter 8Table 8.1 Time of flight,
7 Chapter 9Table 9.1 Non‐zero Lagrange brackets for a perturbed elliptic orbit.Table 9.2 The oblateness parameter,
8 1Table A.1 Coefficients of the Runge‐Kutta 4(5) algorithm
List of Illustrations
1 Chapter 1Figure 1.1 Decay in the orbit due to atmospheric drag for a spacecraft initi...Figure 1.2 Decay in the orbit due to atmospheric drag for a spacecraft initi...Figure
