Classical Dynamics

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ISBN: 9780486696904 | 0486696901
Cover: Paperback
Copyright: 7/7/1997

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Graduate-level text for science and technology students provides strong background in the more abstract and intellectually satisfying areas of dynamical theory. Topics include d'Alembert's principle and the idea of virtual work, Hamilton's equations, Hamilton-Jacobi theory, canonical transformations, more. Problems and references at chapter ends. 1977 edition.

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
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Classical Dynamics

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Table of Contents

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