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Preface | |

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Fundamentals of Newtonian Mechanics | |

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Historical Survey of Mechanics | |

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Newton's Laws | |

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Impulse and Momentum | |

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Moment of a Force and Angular Momentum | |

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Work and Energy | |

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Energy Diagrams | |

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Systems of Particles | |

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The Two-Body Central Force Problem | |

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The Inverse Square Law. Orbits of Planets and Satellites | |

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Scattering by a Repulsive Central Force | |

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Problems | |

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Suggested References | |

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Fundamentals of Analytical Mechanics | |

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Degrees of Freedom. Generalized Coordinates | |

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Systems with Constraints | |

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The Stationary Value of a Function | |

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The Stationary Value of a Definite Integral | |

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The Principle of Virtual Work | |

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D'Alembert's Principle | |

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Hamilton's Principle | |

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Lagrange's Equations of Motion | |

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Lagrange's Equations for Impulsive Forces | |

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Conservation Laws | |

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Routh's Method for the Ignoration of Coordinates | |

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Rayleigh's Dissipation Function | |

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Hamilton's Equations | |

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Problems | |

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Suggested References | |

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Motion Relative to Rotating Reference Frames | |

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Transformation of Coordinates | |

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Rotating Coordinate Systems | |

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Expressions for the Motion in Terms of Moving Reference Frames | |

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Motion Relative to the Rotating Earth | |

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Motion of a Free Particle Relative to the Rotating Earth | |

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Foucault's Pendulum | |

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Problems | |

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Suggested References | |

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Rigid Body Dynamics | |

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Kinematics of a Rigid Body | |

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The Linear and Angular Momentum of a Rigid Body | |

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Translation Theorem for the Angular Momentum | |

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The Kinetic Energy of a Rigid Body | |

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Principal Axes | |

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The Equations of Motion for a Rigid Body | |

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Euler's Equations of Motion | |

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Euler's Angles | |

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Moment-Free Inertially Symmetric Body | |

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General Case of a Moment-Free Body | |

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Motion of a Symmetric Top | |

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The Lagrangian Equations for Quasi-Coordinates | |

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The Equations of Motion Referred to an Arbitrary System of Axes | |

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The Rolling of a Coin | |

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Problems | |

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Suggested References | |

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Behavior of Dynamical Systems. Geometric Theory | |

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Fundamental Concepts | |

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Motion of Single-Degree-of-Freedom Autonomous Systems about Equilibrium Points | |

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Conservative Systems. Motion in the Large | |

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The Index of Poincare | |

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Limit Cycles of Poincare | |

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Problems | |

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Suggested References | |

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Stability of Multi-Degree-of-Freedom Autonomous Systems | |

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General Linear Systems | |

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Linear Autonomous Systems | |

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Stability of Linear Autonomous Systems. Routh-Hurwitz Criterion | |

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The Variational Equations | |

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Theorem on the First-Approximation Stability | |

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Variation from Canonical Systems. Constant Coefficients | |

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The Liapunov Direct Method | |

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Geometric Interpretation of the Liapunov Direct Method | |

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Stability of Canonical Systems | |

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Stability in the Presence of Gyroscopic and Dissipative Forces | |

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Construction of Liapunov Functions for Linear Autonomous Systems | |

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Problems | |

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Suggested References | |

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Nonautonomous Systems | |

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Linear Systems with Periodic Coefficients. Floquet's Theory | |

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Stability of Variational Equations with Periodic Coefficients | |

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Orbital Stability | |

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Variation from Canonical Systems. Periodic Coefficients | |

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Second-Order Systems with Periodic Coefficients | |

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Hill's Infinite Determinant | |

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Mathieu's Equation | |

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The Liapunov Direct Method | |

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Suggested References | |

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Analytical Solutions by Perturbation Techniques | |

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The Fundamental Perturbation Technique | |

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Secular Terms | |

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Lindstedt's Method | |

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The Krylov-Bogoliubov-Mitropolsky (KBM) Method | |

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A Perturbation Technique Based on Hill's Determinants | |

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Periodic Solutions of Nonautonomous Systems. Duffing's Equation | |

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The Method of Averaging | |

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Problems | |

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Suggested References | |

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Transformation Theory. The Hamilton-Jacobi Equation | |

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The Principle of Least Action | |

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Contact Transformations | |

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Further Extensions of the Concept of Contact Transformations | |

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Integral Invariants | |

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The Lagrange and Poisson Brackets | |

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Infinitesimal Contact Transformations | |

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The Hamilton-Jacobi Equation | |

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Separable Systems | |

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Action and Angle Variables | |

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Perturbation Theory | |

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Problems | |

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Suggested References | |

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The Gyroscope: Theory and Applications | |

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Oscillations of a Symmetric Gyroscope | |

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Effect of Gimbal Inertia on the Motion of a Free Gyroscope | |

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Effect of Rotor Shaft Flexibility on the Frequency of Oscillation of a Free Gyroscope | |

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The Gyrocompass | |

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The Gyropendulum. Schuler Tuning | |

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Rate and Integrating Gyroscopes | |

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Problems | |

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Suggested References | |

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Problems in Celestial Mechanics | |

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Kepler's Equation. Orbit Determination | |

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The Many-Body Problem | |

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The Three-Body Problem | |

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The Restricted Three-Body Problem | |

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Stability of Motion Near the Lagrangian Points | |

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The Equations of Relative Motion. Disturbing Function | |

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Gravitational Potential and Torques for an Arbitrary Body | |

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Precession and Nutation of the Earth's Polar Axis | |

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Variation of the Orbital Elements | |

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The Resolution of the Disturbing Function | |

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Problems | |

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Suggested References | |

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Problems in Spacecraft Dynamics | |

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Transfer Orbits. Changes in the Orbital Elements Due to a Small Impulse | |

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Perturbations of a Satellite Orbit in the Gravitational Field of an Oblate Planet | |

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The Effect of Atmospheric Drag on Satellite Orbits | |

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The Attitude Motion of Orbiting Satellites. General Considerations | |

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The Attitude Stability of Earth-Pointing Satellites | |

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The Attitude Stability of Spinning Symmetrical Satellites | |

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Variable-Mass Systems | |

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Rocket Dynamics | |

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Problems | |

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Suggested References | |

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Dyadics | |

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Elements of Topology and Modern Analysis | |

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Sets and Functions | |

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Metric Spaces | |

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Topological Spaces | |

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Suggested References | |

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Name Index | |

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Subject Index | |