Orbital Mechanics for Engineering Students

PrefaceAcknowledgmentsChapter 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 1.8.1 Runge-Kutta methods 1.8.2 Heun’s Predictor-Corrector method 1.8.3 Runge-Kutta with variable step size Problems List of Key TermsChapter 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 2.12.1 Lagrange points 2.12.2 Jacobi constant Problems List of Key TermsChapter 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 Problems List of Key TermsChapter 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 Problems List of Key TermsChapter 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 Problems List of Key TermsChapter 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 Problems List of Key TermsChapter 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 Problems List of Key TermsChapter 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 Problems List of Key TermsChapter 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 9.5.1 Parallel axis theorem 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 List of Key TermsChapter 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 10.8.1 Radial release 10.9 Gyroscopic attitude control 10.10 Gravity gradient stabilization Problems List of Key TermsChapter 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 11.6.1 Lagrange multiplier Problems List of Key TermsAppendix A Physical dataAppendix B A road mapAppendix C Numerical intergration of the n-body equations of motionAppendix D MATLAB® algorithmsAppendix E Gravitational potential energy of a sphereReferencesIndex