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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 | |