| Preface | p. vii |
| Fundamentals of Newtonian Mechanics | p. 1 |
| Historical Survey of Mechanics | p. 1 |
| Newton's Laws | p. 9 |
| Impulse and Momentum | p. 12 |
| Moment of a Force and Angular Momentum | p. 12 |
| Work and Energy | p. 14 |
| Energy Diagrams | p. 17 |
| Systems of Particles | p. 21 |
| The Two-Body Central Force Problem | p. 25 |
| The Inverse Square Law. Orbits of Planets and Satellites | p. 30 |
| Scattering by a Repulsive Central Force | p. 37 |
| Problems | p. 40 |
| Suggested References | p. 44 |
| Fundamentals of Analytical Mechanics | p. 45 |
| Degrees of Freedom. Generalized Coordinates | p. 46 |
| Systems with Constraints | p. 48 |
| The Stationary Value of a Function | p. 53 |
| The Stationary Value of a Definite Integral | p. 55 |
| The Principle of Virtual Work | p. 59 |
| D'Alembert's Principle | p. 65 |
| Hamilton's Principle | p. 66 |
| Lagrange's Equations of Motion | p. 72 |
| Lagrange's Equations for Impulsive Forces | p. 79 |
| Conservation Laws | p. 82 |
| Routh's Method for the Ignoration of Coordinates | p. 85 |
| Rayleigh's Dissipation Function | p. 88 |
| Hamilton's Equations | p. 91 |
| Problems | p. 97 |
| Suggested References | p. 100 |
| Motion Relative to Rotating Reference Frames | p. 101 |
| Transformation of Coordinates | p. 102 |
| Rotating Coordinate Systems | p. 104 |
| Expressions for the Motion in Terms of Moving Reference Frames | p. 110 |
| Motion Relative to the Rotating Earth | p. 112 |
| Motion of a Free Particle Relative to the Rotating Earth | p. 114 |
| Foucault's Pendulum | p. 116 |
| Problems | p. 119 |
| Suggested References | p. 121 |
| Rigid Body Dynamics | p. 122 |
| Kinematics of a Rigid Body | p. 123 |
| The Linear and Angular Momentum of a Rigid Body | p. 126 |
| Translation Theorem for the Angular Momentum | p. 130 |
| The Kinetic Energy of a Rigid Body | p. 132 |
| Principal Axes | p. 134 |
| The Equations of Motion for a Rigid Body | p. 137 |
| Euler's Equations of Motion | p. 138 |
| Euler's Angles | p. 140 |
| Moment-Free Inertially Symmetric Body | p. 143 |
| General Case of a Moment-Free Body | p. 147 |
| Motion of a Symmetric Top | p. 149 |
| The Lagrangian Equations for Quasi-Coordinates | p. 157 |
| The Equations of Motion Referred to an Arbitrary System of Axes | p. 160 |
| The Rolling of a Coin | p. 162 |
| Problems | p. 164 |
| Suggested References | p. 169 |
| Behavior of Dynamical Systems. Geometric Theory | p. 170 |
| Fundamental Concepts | p. 171 |
| Motion of Single-Degree-of-Freedom Autonomous Systems about Equilibrium Points | p. 178 |
| Conservative Systems. Motion in the Large | p. 189 |
| The Index of Poincare | p. 195 |
| Limit Cycles of Poincare | p. 198 |
| Problems | p. 206 |
| Suggested References | p. 208 |
| Stability of Multi-Degree-of-Freedom Autonomous Systems | p. 209 |
| General Linear Systems | p. 210 |
| Linear Autonomous Systems | p. 217 |
| Stability of Linear Autonomous Systems. Routh-Hurwitz Criterion | p. 222 |
| The Variational Equations | p. 225 |
| Theorem on the First-Approximation Stability | p. 226 |
| Variation from Canonical Systems. Constant Coefficients | p. 229 |
| The Liapunov Direct Method | p. 231 |
| Geometric Interpretation of the Liapunov Direct Method | p. 239 |
| Stability of Canonical Systems | p. 243 |
| Stability in the Presence of Gyroscopic and Dissipative Forces | p. 252 |
| Construction of Liapunov Functions for Linear Autonomous Systems | p. 258 |
| Problems | p. 260 |
| Suggested References | p. 262 |
| Nonautonomous Systems | p. 263 |
| Linear Systems with Periodic Coefficients. Floquet's Theory | p. 264 |
| Stability of Variational Equations with Periodic Coefficients | p. 271 |
| Orbital Stability | p. 272 |
| Variation from Canonical Systems. Periodic Coefficients | p. 273 |
| Second-Order Systems with Periodic Coefficients | p. 277 |
| Hill's Infinite Determinant | p. 280 |
| Mathieu's Equation | p. 282 |
| The Liapunov Direct Method | p. 288 |
| Suggested References | p. 292 |
| Analytical Solutions by Perturbation Techniques | p. 293 |
| The Fundamental Perturbation Technique | p. 294 |
| Secular Terms | p. 297 |
| Lindstedt's Method | p. 299 |
| The Krylov-Bogoliubov-Mitropolsky (KBM) Method | p. 302 |
| A Perturbation Technique Based on Hill's Determinants | p. 309 |
| Periodic Solutions of Nonautonomous Systems. Duffing's Equation | p. 313 |
| The Method of Averaging | p. 322 |
| Problems | p. 327 |
| Suggested References | p. 328 |
| Transformation Theory. The Hamilton-Jacobi Equation | p. 329 |
| The Principle of Least Action | p. 330 |
| Contact Transformations | p. 334 |
| Further Extensions of the Concept of Contact Transformations | p. 339 |
| Integral Invariants | p. 346 |
| The Lagrange and Poisson Brackets | p. 349 |
| Infinitesimal Contact Transformations | p. 352 |
| The Hamilton-Jacobi Equation | p. 355 |
| Separable Systems | p. 361 |
| Action and Angle Variables | p. 365 |
| Perturbation Theory | p. 372 |
| Problems | p. 378 |
| Suggested References | p. 380 |
| The Gyroscope: Theory and Applications | p. 381 |
| Oscillations of a Symmetric Gyroscope | p. 382 |
| Effect of Gimbal Inertia on the Motion of a Free Gyroscope | p. 386 |
| Effect of Rotor Shaft Flexibility on the Frequency of Oscillation of a Free Gyroscope | p. 389 |
| The Gyrocompass | p. 393 |
| The Gyropendulum. Schuler Tuning | p. 398 |
| Rate and Integrating Gyroscopes | p. 403 |
| Problems | p. 406 |
| Suggested References | p. 407 |
| Problems in Celestial Mechanics | p. 408 |
| Kepler's Equation. Orbit Determination | p. 409 |
| The Many-Body Problem | p. 413 |
| The Three-Body Problem | p. 416 |
| The Restricted Three-Body Problem | p. 420 |
| Stability of Motion Near the Lagrangian Points | p. 425 |
| The Equations of Relative Motion. Disturbing Function | p. 428 |
| Gravitational Potential and Torques for an Arbitrary Body | p. 430 |
| Precession and Nutation of the Earth's Polar Axis | p. 438 |
| Variation of the Orbital Elements | p. 442 |
| The Resolution of the Disturbing Function | p. 447 |
| Problems | p. 450 |
| Suggested References | p. 451 |
| Problems in Spacecraft Dynamics | p. 452 |
| Transfer Orbits. Changes in the Orbital Elements Due to a Small Impulse | p. 453 |
| Perturbations of a Satellite Orbit in the Gravitational Field of an Oblate Planet | p. 457 |
| The Effect of Atmospheric Drag on Satellite Orbits | p. 463 |
| The Attitude Motion of Orbiting Satellites. General Considerations | p. 466 |
| The Attitude Stability of Earth-Pointing Satellites | p. 470 |
| The Attitude Stability of Spinning Symmetrical Satellites | p. 475 |
| Variable-Mass Systems | p. 483 |
| Rocket Dynamics | p. 487 |
| Problems | p. 491 |
| Suggested References | p. 492 |
| Dyadics | p. 494 |
| Elements of Topology and Modern Analysis | p. 497 |
| Sets and Functions | p. 498 |
| Metric Spaces | p. 501 |
| Topological Spaces | p. 504 |
| Suggested References | p. 506 |
| Name Index | p. 507 |
| Subject Index | p. 511 |
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