| |
| |
| Preface to the Second Edition | |
| |
| |
| Preface to the First Edition | |
| |
| |
| Basic Mechanics | |
| |
| |
| Particle Kinematics | |
| |
| |
| Introduction | |
| |
| |
| Particle Position Description | |
| |
| |
| Vector Differentiation | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Newtonian Mechanics | |
| |
| |
| Introduction | |
| |
| |
| Newton's Laws | |
| |
| |
| Single Particle Dynamics | |
| |
| |
| Dynamics of a System of Particles | |
| |
| |
| Dynamics of a Continuous System | |
| |
| |
| Rocket Problem | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Rigid Body Kinematics | |
| |
| |
| Introduction | |
| |
| |
| Direction Cosine Matrix | |
| |
| |
| Euler Angles | |
| |
| |
| Principal Rotation Vector | |
| |
| |
| Euler Parameters | |
| |
| |
| Classical Rodrigues Parameters | |
| |
| |
| Modified Rodrigues Parameters | |
| |
| |
| Other Attitude Parameters | |
| |
| |
| Homogeneous Transformations | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Kulerian Mechanics | |
| |
| |
| Introduction | |
| |
| |
| Rigid Body Dynamics | |
| |
| |
| Torque-Free Rigid Body Rotation | |
| |
| |
| Dual-Spin Spacecraft | |
| |
| |
| Momentum Exchange Devices | |
| |
| |
| Gravity Gradient Satellite | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Generalized Methods of Analytical Dynamics | |
| |
| |
| Introduction | |
| |
| |
| Generalized Coordinates | |
| |
| |
| D'Alembert's Principle | |
| |
| |
| Lagrangian Dynamics | |
| |
| |
| Quasi Coordinates | |
| |
| |
| Cyclic Coordinates | |
| |
| |
| Final Observations | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Variational Methods in Analytical Dynamics | |
| |
| |
| Introduction | |
| |
| |
| Fundamentals of Variational Calculus | |
| |
| |
| Hamilton's Variational Principles | |
| |
| |
| Hamilton's Principal Function | |
| |
| |
| Some Classical Applications of Hamilton's Principle to Distributed Parameter Systems | |
| |
| |
| Explicit Generalizations of Lagrange's Equations for Hybrid Coordinate Systems | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Hamilton's Generalized Formulations of Analytical Dynamics | |
| |
| |
| Introduction | |
| |
| |
| Hamittonian Function | |
| |
| |
| Relationship of Hamiltonian Function to Work/Energy Integral | |
| |
| |
| Hamilton's Canonical Equations | |
| |
| |
| Poisson's Brackets | |
| |
| |
| Canonical Coordinate Transformations | |
| |
| |
| Perfect Differential Criterion for Canonical Transformations | |
| |
| |
| Transformation Jacobian Perspective on Canonical Transformations | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Nonlinear Spacecraft Stability and Control | |
| |
| |
| Introduction | |
| |
| |
| Nonlinear Stability Analysis | |
| |
| |
| Generating Lyapunov Functions | |
| |
| |
| Nonlinear Feedback Control Laws | |
| |
| |
| Lyapunov Optimal Control Laws | |
| |
| |
| Linear Closed-Loop Dynamics | |
| |
| |
| Reaction Wheel Control Devices | |
| |
| |
| Variable Speed Control Moment Gyroscopes | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Celestial Mechanics | |
| |
| |
| Classical Two-Body Problem | |
| |
| |
| Introduction | |
| |
| |
| Geometry of Conic Sections | |
| |
| |
| Coordinate Systems | |
| |
| |
| Relative Two-Body Equations of Motion | |
| |
| |
| Fundamental Integrals | |
| |
| |
| Classical Solutions | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Restricted Three-Body Problem | |
| |
| |
| Introduction | |
| |
| |
| Lagrange's Three-Body Solution | |
| |
| |
| Circular Restricted Three-Body Problem | |
| |
| |
| Periodic Stationary Orbits | |
| |
| |
| Disturbing Function | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Gravitational Potential Field Models | |
| |
| |
| Introduction | |
| |
| |
| Gravitational Potential of Finite Bodies | |
| |
| |
| MacCullagh's Approximation | |
| |
| |
| Spherical Harmonic Gravity Potential | |
| |
| |
| Multibody Gravitational Acceleration | |
| |
| |
| Spheres of Gravitational Influence | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Perturbation Methods | |
| |
| |
| Introduction | |
| |
| |
| Encke's Method | |
| |
| |
| Variation of Parameters | |
| |
| |
| State Transition and Sensitivity Matrix | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Transfer Orbits | |
| |
| |
| Introduction | |
| |
| |
| Minimum Energy Orbit | |
| |
| |
| Hohmann Transfer Orbit | |
| |
| |
| Lambert's Problem | |
| |
| |
| Rotating the Orbit Plane | |
| |
| |
| Patched-Conic Orbit Solution | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Spacecraft Formation Flying | |
| |
| |
| Introduction | |
| |
| |
| General Relative Orbit Description | |
| |
| |
| Cartesian Coordinate Description | |
| |
| |
| Orbit Element Difference Description | |
| |
| |
| Relative Motion State Transition Matrix | |
| |
| |
| Linearized Relative Orbit Motion | |
| |
| |
| J<sub>2</sub>-Invariant Relative Orbits | |
| |
| |
| Relative Orbit Control Methods | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| Transport Theorem Derivation Using Linear Algebra | |
| |
| |
| Various Euler Angle Transformations | |
| |
| |
| MRP Identity Proof | |
| |
| |
| Conic Section Transformations | |
| |
| |
| Numerical Subroutines Library | |
| |
| |
| First-Order Mapping Between Mean and Osculating Orbit Elements | |
| |
| |
| Direct Linear Mapping Between Cartesian Hill Frame Coordinates and Orbit Element Differences | |
| |
| |
| Hamel Coefficients for the Rotational Morion of a Rigid Body | |
| |
| |
| Index | |
| |
| |
| Supporting Materials | |