Methods of analytical dynamics

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Title page Preface Chapter 1 Fundamentals of Newtonian Mechanics 1.1 Historical Survey of Mechanics 1.2 Newton's Laws 1.3 Impulse and Momentum 1.4 Moment of a Force and Angular Momentum 1.5 Work and Energy 1.6 Energy Diagrams 1.7 Systems of Particles 1.8 The Two-Body Central Force Problem 1.9 The Inverse Square Law. Orbits of Planets and Satellites 1.10 Scattering by a Repulsive Central Force Problems Suggested References Chapter 2 Fundamentals of Analytical Mechanics 2.1 Degrees of Freedom. Generalized Coordinates 2.2 Systems with Constraints 2.3 The Stationary Value of a Function 2.4 The Stationary Value of a Definite Integral 2.5 The Principle of Virtual Work 2.6 D'Alembert's Principle 2.7 Hamilton 's Principle 2.8 Lagrange's Equations of Motion 2.9 Lagrange's Equations for Impulsive Forces 2.10 Conservation Laws 2.11 Routh's Method for the Ignoration of Coordinates 2.12 Rayleigh's Dissipation Function 2.13 Hamilton's Equations Problems Suggested References Chapter 3 Motion Relative to Rotating Reference Frames 3.1 Transformation of Coordinates 3.2 Rotating Coordinate Systems 3.3 Expressions for the Motion in Terms of Moving Reference Frames 3.4 Motion Relative to the Rotating Earth 3.5 Motion of a Free Particle Relative to the Rotating Earth 3.6 Foucault's Pendulum Problems Suggested References Chapter 4 Rigid Body Dynamics 4.1 Kinematics of a Rigid Body 4.2 The Linear and Angular Momentum of a Rigid Body 4.3 Translation Theorem for the Angular Momentum 4.4 The Kinetic Energy of a Rigid Body 4.5 Principal Axes 4.6 The Equations of Motion for a Rigid Body 4.7 Euler's Equations of Motion 4.8 Euler's Angles 4.9 Moment-Free Inertially Symmetric Body 4.10 General Case of a Moment-Free Body 4.11 Motion of a Symmetric Top 4.12 The Lagrangian Equations for Quasi-Coordinates 4.13 The Equations of Motion Referred to an Arbitrary System of Axes 4.14 The Rolling of a Coin Problems Suggested References Chapter 5 Behavior of Dynamical Systems. Geometric Theory 5.1 Fundamental Concepts 5.2 Motion of Single-Degree-of-Freedom Autonomous Systems about Equilibrium Points 5.3 Conservative Systems. Motion in the Large 5.4 The Index of Poincaré 5.5 Limit Cycles of Poincaré Problems Suggested References Chapter 6 Stability of Multi-Degree-of-Freedom Autonomous Systems 6.1 General Linear Systems 6.2 Linear Autonomous Systems 6.3 Stability of Linear Autonomous Systems. Routh-Hurwitz Criterion 6.4 The Variational Equations 6.5 Theorem on the First-Approximation Stability 6.6 Variation from Canonical Systems. Constant Coefficients 6.7 The Liapunov Direct Method 6.8 Geometrie Interpretation of the Liapunov Direct Method 6.9 Stability of Canonical Systems 6.10 Stability in the Presence of Gyroscopic and Dissipative Forces 6.11 Construction of Liapunov Functions for Linear Autonomous Systems Problems Suggested References Chapter 7 Nonautonomous Systems 7.1 Linear Systems with Periodic Coefficients. Floquet's Theory 7.2 Stability of Variational Equations with Periodic Coefficients 7.3 Orbital Stability 7.4 Variation from Canonical Systems. Periodic Coefficients 7.5 Second-Order Systems with Periodic Coefficients 7.6 Hill's Infinite Determinant 7.7 Mathieu's Equation 7.8 The Liapunov Direct Method Suggested References Chapter 8 Analytical Solutions by Perturbation Techniques 8.1 The Fundamental Perturbation Technique 8.2 Secular Terms 8.3 Lindstedt's Method 8.4 The Krylov-Bogoliubov-Mitropolsky (KBM) Method 8.5 A Perturbation Technique Based on Hill's Determinants 8.6 Periodic Solutions of Nonautonomous Systems. Duffing's Equation 8.7 The Method of Averaging Problems Suggested References Chapter 9 Transformation Theory. The Hamilton-Jacobi Equation 9.1 The Principle of Least Action 9.2 Contact Transformations 9.3 Further Extensions of the Concept of Contact Transformations 9.4 Integral Invariants 9.5 The Lagrange and Poisson Brackets 9.6 Infinitesimal Contact Transformations 9.7 The Hamilton-Jacobi Equation 9.8 Separable Systems 9.9 Action and Angle Variables 9.10 Perturbation Theory Problems Suggested References Chapter 10 The Gyroscope: Theory and Applications 10.1 Oscillations of a Symmetric Gyroscope 10.2 Effect of Gimbal Inertia on the Motion of a Free Gyroscope 10.3 Effect of Rotor Shaft Flexibility on the Frequency of Oscillation of a Free Gyroscope 10.4 The Gyrocompass 10.5 The Gyropendulum. Schuler Tuning 10.6 Rate and 1ntegrating Gyroscopes Problems Suggested References Chapter 11 Problems in Celestial Mechanics 11.1 Kepler's Equation. Orbit Determination 11.2 The Many-Body Problem 11.3 The Three-Body Problem 11.4 The Restricted Three-Body Problem 11.5 Stability of Motion Near the Lagrangian Points 11.6 The Equations of Relative Motion. Disturbing Function 11.7 Gravitational Potential and Torques for an Arbitrary Body 11.8 Precession and Nutation of the Earth's Polar Axis 11.9 Variation of the Orbital Elements 11.10 The Resolution of the Disturbing Function Problems Suggested References Chapter 12 Problems in Spacecraft Dynamics 12.1 Transfer Orbits. Changes in the Orbital Elements Due to a Small Impulse 12.2 Perturbations of a Satellite Orbit in the Gravitational Field of an Oblate Planet 12.3 The Effect of Atmospheric Drag on Satellite Orbits 12.4 The Attitude Motion of Orbiting Satellites. General Considerations 12.5 The Attitude Stability of Earth-Pointing Satellites 12.6 The Attitude Stability of Spinning Symmetrical Satellites 12.7 Variable-Mass Systems 12.8 Rocket Dynamics Problems Suggested References Appendix A Dyadics Appendix B Elements of Topology and Modern Analysis B.1 Sets and Functions B.2 Metric Spaces B.3 Topological Spaces Suggested References Name Index Subject Index