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Table of Contents Preface##xiii Part 1#Basic Mechanics Chapter 1.#Particle Kinematics#3 1.1#Introduction#3 1.2#Particle Position Description#3 1.3#Vector Differentiation#8 References##19 Problems##20 Chapter 2.#Newtonian Mechanics#27 2.1#Introduction#27 2.2#Newtons Laws#27 2.3#Single Particle Dynamics#31 2.4#Dynamics of a System of Particles#43 2.5#Dynamics of a Continuous System#53 2.6#Rocket Problem#58 References##63 Problems##63 Chapter 3.#Rigid Body Kinematics#71 3.1#Introduction#71 3.2#Direction Cosine Matrix#72 3.3#Euler Angles#78 3.4#Principal Rotation Vector#87 3.5#Euler Parameters#95 3.6#Classical Rodrigues Parameters#102 3.7#Modified Rodrigues Parameters#107 3.8#Other Attitude Parameters#115 3.9#Homogeneous Transformations#119 References##000 Problems##000 Chapter 4.#Eulerian Mechanics#127 4.1#Introduction#127 4.2#Rigid Body Dynamics#127 4.3#Torque-Free Rigid Body Rotation#142 4.4#Momentum Exchange Devices#151 4.5#Gravity Gradient Satellite#160 References##170 Problems##171 Chapter 5.#Generalized Methods of Analytical Dynamics#177 5.1#Introduction#177 5.2#Generalized Coordinates#177 5.3#DAlemberts Principle#180 5.4#Lagrangian Dynamics#204 References##231 Problems##231 Chapter 6.#Variational Methods in Analytical Dynamics#237 6.1#Introduction#237 6.2#Fundamentals of Variational Calculus#237 6.3#Hamiltons Variational Principles#241 6.4#Hamiltons Principal Function#245 6.5#Some Classical Applications of Hamiltons Principle to Distributed Parameter Systems#250 6.6#Explicit Generalizations of Lagranges Equations for Hybrid Coordinate Systems#254 References##261 Problems##261 Chapter 7.#Hamiltons Generalized Formulations of Analytical Dynamics#265 7.1#Introduction#265 7.2#Hamiltonian Function#265 7.3#Ignorable Coordinates#270 7.4#Relationship of Hamiltonian Function to WorkEnergy Integral#271 7.5#Hamiltons Canonical Equations#276 7.6#Poissons Brackets#280 7.7#Canonical Coordinate Transformations#283 7.8#Perfect Differential Criterion for Canonical Transformations#287 7.9#Transformation Jacobian Perspective on Canonical Transformations#290 References##292 Problems##292 Chapter 8.#Nonlinear Spacecraft Stability and Control#295 8.1#Introduction#295 8.2#Nonlinear Stability Analysis#295 8.3#Generating Lyapunov Functions#310 8.4#Nonlinear Feedback Control Laws#325 8.5#Lyapunov Optimal Control Laws#339 8.6#Linear Closed-Loop Dynamics#345 8.7#Reaction Wheel Control Devices#351 8.8#Variable Speed Control Moment Gyroscopes#353 References##372 Problems##374 Part 2#Celestial Mechanics Chapter 9.#Classical Two-Body Problem#381 9.1#Introduction#381 9.2#Geometry of Conic Sections#382 9.3#Relative Two-Body Equations of Motion#390 9.4#Fundamental Integrals#392 9.5#Classical Solutions#404 References##420 Problems##421 Chapter 10.#Restricted Three-Body Problem#423 10.1#Introduction#423 10.2#Lagranges Three-Body Solution#423 10.3#Circular Restricted Three-Body Problem#438 10.4#Periodic Stationary Orbits#458 10.5#Disturbing Function#460 References##463 Problems##463 Chapter 11.#Gravitational Potential Field Models#465 11.1#Introduction#465 11.2#Gravitational Potential of Finite Bodies#466 11.3#MacCullaghs Approximation#469 11.4#Spherical Harmonic Gravity Potential#472 11.5#Multibody Gravitational Acceleration#483 11.6#Spheres of Gravitational Influence#485 References##488 Problems##488 Chapter 12.#Perturbation Methods#489 12.1#Introduction#489 12.2#Enckes Method#490 12.3#Variation of Parameters#492 12.4#State Transition and Sensitivity Matrix#525 References##540 Problems##541 Chapter 13.#Transfer Orbits#545 13.1#Introduction#545 13.2#Minimum Energy Orbit#545 13.3#Hohmann Transfer Orbit#549 13.4#Lamberts Problem #554 13.5#Rotating the Orbit Plane #563 13.6#Patched-Conic Orbit Solution#568 References##589 Problems##589 Chapter 14.#Spacecraft Formation Flying#593 14.1#Introduction#593 14.2#General Relative Orbit Description#594 14.3#Cartesian Coordinate Description#596 14.4#Orbit Element Difference Description#604 14.5#Relative Motion State Transition Matrix#613 14.6#Linearized Relative Orbit Motion#618 14.7#J_2-Invariant Relative Orbits#628 14.8#Relative Orbit Control Methods#649 References##669 Problems##671 Appendix A.#Transport Theorem Derivation Using Linear Algebra#675 Appendix B.#Various Euler Angle Transformations#679 Appendix C.#MRP Identity Proof#683 Appendix D.#Conic Section Transformations#685 Appendix E.#MATLAB M-Files#689 Appendix F.#First-Order Mapping Between Mean and Osculating Orbit Elements#693 Appendix G.#Direct Linear Mapping Between Cartesian Hill Frame Coordinates and Orbit Element Differences#697 Appendix H.#Hamel Coefficients for the Rotational Motion of a Rigid Body#699 Index##705
Library of Congress Subject Headings for this publication: Celestial mechanics, Differentiable dynamical systems