| Preface | |
| Introductory concepts | |
| The Mechanical System | |
| Equations of motion | |
| Units | |
| Generalized Coordinates | |
| Degrees of freedom | |
| Generalized Coordinates | |
| Configuration space | |
| Example | |
| Constraints | |
| Holonomic constraints | |
| Nonholonomic constraints | |
| Unilateral constraints | |
| Example | |
| Virtual Work | |
| Virtual displacement | |
| Virtual work | |
| Principle of virtual work | |
| D'Alembert's principle | |
| Generalized force | |
| Examples | |
| Energy and Momentum | |
| Potential energy | |
| Work and kinetic energy | |
| Conservation of energy | |
| Equilibrium and stability | |
| Kinetic energy of a system | |
| Angular momentum | |
| Generalized momentum | |
| Example | |
| Lagrange's Equations | |
| Derivation of Lagrange's Equations | |
| Kinetic energy | |
| Lagrange's equations | |
| Form of the equations of motion | |
| Nonholonomic systems | |
| Examples | |
| Spherical pendulum | |
| Double pendulum | |
| Lagrange multipliers and constraint forces | |
| Particle in whirling tube | |
| Particle with moving support | |
| Rheonomic constrained system | |
| Integrals of the Motion | |
| Ignorable coordinates | |
| Example--the Kepler problem | |
| Routhian function | |
| Conservative systems | |
| Natural systems | |
| Liouville's system | |
| Examples | |
| Small Oscillations | |
| Equations of motion | |
| Natural modes | |
| Principal coordinates | |
| Orthogonality | |
| Repeated roots | |
| Initial conditions | |
| Example | |
| Special applications of Lagrange's Equations | |
| Rayleigh's Dissipation function | |
| Impulsive Motion | |
| Impulse and momentum | |
| Lagrangian method | |
| Ordinary constraints | |
| Impulsive constraints | |
| Energy considerations | |
| Quasi-coordinates | |
| Examples | |
| Gyroscopic systems | |
| Gyroscopic forces | |
| Small motions | |
| Gyroscopic stability | |
| Examples | |
| Velocity-Dependent Potentials | |
| Electromagnetic forces | |
| Gyroscopic forces | |
| Example | |
| Hamilton's Equations | |
| Hamilton's Principle | |
| Stationary values of a function | |
| Constrained stationary values | |
| Stationary value of a definite integral | |
| Example--the brachistochrone problem Example--geodesic path | |
| Case of n dependent variables | |
| Hamilton's principle | |
| Nonholonomic systems | |
| Multiplier rule | |
| Hamilton's Equations | |
| Derivation of Hamilton's equations | |
| The form of the Hamiltonian function | |
| Legendre transformation | |
| Examples | |
| Other Variational Principles | |
| Modified Hamilton's principle | |
| Principle of least action | |
| Example | |
| Phase Space | |
| Trajectories | |
| Extended phase space | |
| Liouville's theorem | |
| Hamilton-Jacobi Theory | |
| Hamilton's Principal Function | |
| The canonical integral | |
| Pfaffian differential forms | |
| The Hamilton-Jacobi Equation | |
| Jacobi's theorem | |
| Conservative systems and ignorable coordinates | |
| Examples | |
| Separability | |
| Liouville's system | |
| Stackel's theorem | |
| Example | |
| Canonical Transformations | |
| Differential Forms and Generating Functions | |
| Canonical transformations | |
| Principal forms of generating functions | |
| Further comments on the Hamilton-Jacobi method | |
| Examples | |
| Special Transformations | |
| Some simple transformations | |
| Homogeneous canonical transformations | |
| Point transformations | |
| Momentum transformations | |
| Examples | |
| Lagrange and Poisson Brackets | |
| Lagrange brackets | |
| Poisson brackets | |
| The bilinear covariant | |
| Example | |
| More General Transformations | |
| Necessary conditions | |
| Time transformations | |
| Examples | |
| Matrix Foundations | |
| Hamilton's equations | |
| Symplectic matrices | |
| Example | |
| Further Topics | |
| Infinitesimal canonical transformations | |
| Liouville's theorem | |
| Integral invariants | |
| Introduction to Relativity | |
| Introduction | |
| Galilean transformations | |
| Maxwell's equations | |
| The Ether theory | |
| The principle of relativity | |
| Relativistic Kinematics | |
| The Lorentz transformation equations | |
| Events and simultaneity | |
| Example--Einstein's train | |
| Time dilation | |
| Longitudinal contraction | |
| The invariant interval | |
| Proper time and proper distance | |
| The world line | |
| Example--the twin paradox | |
| Addition of velocities | |
| The relativistic Doppler effect | |
| Examples | |
| Relativistic dynamics | |
| Momentum | |
| Ener | |
| Table of Contents provided by Publisher. All Rights Reserved. |
