Classical Dynamics

By: DONALD T. GREENWOOD

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Paperback | 7 July 1997

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Paperback
368 Pages

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New edition

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20.9 x 13.6 x 1.91

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Graduate-level text provides strong background in more abstract areas of dynamical theory. Hamilton's equations, d'Alembert's principle, Hamilton-Jacobi theory, other topics. Problems and references. Since Lagrange laid the foundation of analytical dynamics some two centuries ago, the discipline has continued to evolve and develop, embracing the theories of Hamilton and Jacobi, Einstein's relativity theory and advanced theories of classical mechanics.This text proposes to give graduate students in science and engineering a strong background in the more abstract and intellectually satisfying areas of dynamical theory. It is assumed that students are familiar with the principles of vectorial mechanics and have some facility in the use of this theory for analysis of systems of particles and for rigid-body rotation in two and three dimensions.After a concise review of basic concepts in Chapter 1, the author proceeds from Lagrange's and Hamilton's equations to Hamilton-Jacobi theory and canonical transformations. Topics include d'Alembert's principle and the idea of virtual work, the derivation of Langrange's equation of motion, special applications of Lagrange's equations, Hamilton's equations, the Hamilton-Jacobi theory, canonical transformations and an introduction to relativity.Problems included at the end of each chapter will help the student greatly in solidifying his grasp of the principal concepts of classical dynamics. An annotated bibliography at the end of each chapter, a detailed table of contents and index, and selected end-of-chapter answers complete this highly instructive text.

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You Can Find This Book In

Non-Fiction Science Physics Relativity Physics Classical Mathematics Dynamics & Statics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Solids Dynamics & Vibration Mathematics

Applied Mathematics Analytical Mechanics Science in General

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.

Classical Dynamics

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Paperback

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