| Preface |
| Introductory concepts / 1： |
| The Mechanical System / 1.1： |
| Equations of motion |
| Units |
| Generalized Coordinates / 1.2： |
| Degrees of freedom |
| Configuration space |
| Example |
| Constraints / 1.3： |
| Holonomic constraints |
| Nonholonomic constraints |
| Unilateral constraints |
| Virtual Work / 1.4： |
| Virtual displacement |
| Virtual work |
| Principle of virtual work |
| D'Alembert's principle |
| Generalized force |
| Examples |
| Energy and Momentum / 1.5： |
| Potential energy |
| Work and kinetic energy |
| Conservation of energy |
| Equilibrium and stability |
| Kinetic energy of a system |
| Angular momentum |
| Generalized momentum |
| Lagrange's Equations / 2： |
| Derivation of Lagrange's Equations / 2.1： |
| Kinetic energy |
| Lagrange's equations |
| Form of the equations of motion |
| Nonholonomic systems |
| Spherical pendulum / 2.2： |
| Double pendulum |
| Lagrange multipliers and constraint forces |
| Particle in whirling tube |
| Particle with moving support |
| Rheonomic constrained system |
| Integrals of the Motion / 2.3： |
| Ignorable coordinates |
| Example--the Kepler problem |
| Routhian function |
| Conservative systems |
| Natural systems |
| Liouville's system |
| Small Oscillations / 2.4： |
| Natural modes |
| Principal coordinates |
| Orthogonality |
| Repeated roots |
| Initial conditions |
| Special applications of Lagrange's Equations / 3： |
| Rayleigh's Dissipation function / 3.1： |
| Impulsive Motion / 3.2： |
| Impulse and momentum |
| Lagrangian method |
| Ordinary constraints |
| Impulsive constraints |
| Energy considerations |
| Quasi-coordinates |
| Gyroscopic systems / 3.3： |
| Gyroscopic forces |
| Small motions |
| Gyroscopic stability |
| Velocity-Dependent Potentials / 3.4： |
| Electromagnetic forces |
| Hamilton's Equations / 4： |
| Hamilton's Principle / 4.1： |
| 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 |
| Multiplier rule |
| Derivation of Hamilton's equations / 4.2： |
| The form of the Hamiltonian function |
| Legendre transformation |
| Other Variational Principles / 4.3： |
| Modified Hamilton's principle |
| Principle of least action |
| Phase Space / 4.4： |
| Trajectories |
| Extended phase space |
| Liouville's theorem |
| Hamilton-Jacobi Theory / 5： |
| Hamilton's Principal Function / 5.1： |
| The canonical integral |
| Pfaffian differential forms |
| The Hamilton-Jacobi Equation / 5.2： |
| Jacobi's theorem |
| Conservative systems and ignorable coordinates |
| Separability / 5.3： |
| Stackel's theorem |
| Canonical Transformations / 6： |
| Differential Forms and Generating Functions / 6.1： |
| Canonical transformations |
| Principal forms of generating functions |
| Further comments on the Hamilton-Jacobi method |
| Special Transformations / 6.2： |
| Some simple transformations |
| Homogeneous canonical transformations |
| Point transformations |
| Momentum transformations |
| Lagrange and Poisson Brackets / 6.3： |
| Lagrange brackets |
| Poisson brackets |
| The bilinear covariant |
| More General Transformations / 6.4： |
| Necessary conditions |
| Time transformations |
| Matrix Foundations / 6.5： |
| Hamilton's equations |
| Symplectic matrices |
| Further Topics / 6.6： |
| Infinitesimal canonical transformations |
| Integral invariants |
| Introduction to Relativity / 7： |
| Introduction / 7.1： |
| Galilean transformations |
| Maxwell's equations |
| The Ether theory |
| The principle of relativity |
| Relativistic Kinematics / 7.2： |
| 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 |
| Relativistic dynamics / 7.3： |
| Momentum |
| Ener |
| Preface |
| Introductory concepts / 1： |
| The Mechanical System / 1.1： |
図書
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