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Preface | |

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Introductory concepts | |

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The Mechanical System | |

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Equations of motion | |

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Units | |

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Generalized Coordinates | |

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Degrees of freedom | |

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Generalized Coordinates | |

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Configuration space | |

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Example | |

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Constraints | |

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Holonomic constraints | |

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Nonholonomic constraints | |

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Unilateral constraints | |

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Example | |

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Virtual Work | |

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Virtual displacement | |

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Virtual work | |

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Principle of virtual work | |

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D'Alembert's principle | |

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Generalized force | |

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Examples | |

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Energy and Momentum | |

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Potential energy | |

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Work and kinetic energy | |

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Conservation of energy | |

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Equilibrium and stability | |

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Kinetic energy of a system | |

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Angular momentum | |

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Generalized momentum | |

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Example | |

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Lagrange's Equations | |

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Derivation of Lagrange's Equations | |

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Kinetic energy | |

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Lagrange's equations | |

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Form of the equations of motion | |

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Nonholonomic systems | |

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Examples | |

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Spherical pendulum | |

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Double pendulum | |

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Lagrange multipliers and constraint forces | |

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Particle in whirling tube | |

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Particle with moving support | |

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Rheonomic constrained system | |

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Integrals of the Motion | |

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Ignorable coordinates | |

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Example--the Kepler problem | |

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Routhian function | |

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Conservative systems | |

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Natural systems | |

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Liouville's system | |

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Examples | |

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Small Oscillations | |

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Equations of motion | |

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Natural modes | |

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Principal coordinates | |

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Orthogonality | |

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Repeated roots | |

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Initial conditions | |

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Example | |

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Special applications of Lagrange's Equations | |

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Rayleigh's Dissipation function | |

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Impulsive Motion | |

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Impulse and momentum | |

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Lagrangian method | |

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Ordinary constraints | |

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Impulsive constraints | |

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Energy considerations | |

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Quasi-coordinates | |

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Examples | |

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Gyroscopic systems | |

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Gyroscopic forces | |

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Small motions | |

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Gyroscopic stability | |

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Examples | |

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Velocity-Dependent Potentials | |

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Electromagnetic forces | |

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Gyroscopic forces | |

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Example | |

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Hamilton's Equations | |

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Hamilton's Principle | |

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Stationary values of a function | |

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Constrained stationary values | |

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Stationary value of a definite integral | |

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Example--the brachistochrone problem Example--geodesic path | |

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Case of n dependent variables | |

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Hamilton's principle | |

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Nonholonomic systems | |

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Multiplier rule | |

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Hamilton's Equations | |

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Derivation of Hamilton's equations | |

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The form of the Hamiltonian function | |

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Legendre transformation | |

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Examples | |

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Other Variational Principles | |

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Modified Hamilton's principle | |

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Principle of least action | |

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Example | |

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Phase Space | |

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Trajectories | |

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Extended phase space | |

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Liouville's theorem | |

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Hamilton-Jacobi Theory | |

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Hamilton's Principal Function | |

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The canonical integral | |

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Pfaffian differential forms | |

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The Hamilton-Jacobi Equation | |

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Jacobi's theorem | |

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Conservative systems and ignorable coordinates | |

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Examples | |

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Separability | |

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Liouville's system | |

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Stackel's theorem | |

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Example | |

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Canonical Transformations | |

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Differential Forms and Generating Functions | |

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Canonical transformations | |

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Principal forms of generating functions | |

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Further comments on the Hamilton-Jacobi method | |

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Examples | |

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Special Transformations | |

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Some simple transformations | |

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Homogeneous canonical transformations | |

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Point transformations | |

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Momentum transformations | |

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Examples | |

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Lagrange and Poisson Brackets | |

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Lagrange brackets | |

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Poisson brackets | |

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The bilinear covariant | |

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Example | |

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More General Transformations | |

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Necessary conditions | |

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Time transformations | |

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Examples | |

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Matrix Foundations | |

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Hamilton's equations | |

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Symplectic matrices | |

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Example | |

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Further Topics | |

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Infinitesimal canonical transformations | |

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Liouville's theorem | |

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Integral invariants | |

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Introduction to Relativity | |

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Introduction | |

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Galilean transformations | |

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Maxwell's equations | |

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The Ether theory | |

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The principle of relativity | |

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Relativistic Kinematics | |

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The Lorentz transformation equations | |

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Events and simultaneity | |

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Example--Einstein's train | |

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Time dilation | |

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Longitudinal contraction | |

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The invariant interval | |

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Proper time and proper distance | |

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The world line | |

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Example--the twin paradox | |

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Addition of velocities | |

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The relativistic Doppler effect | |

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Examples | |

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Relativistic dynamics | |

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Momentum | |

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Ener | |