拉格朗日及汉密尔敦力学LAGRANGIAN AND HAMILTONIAN MECHANICS
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作者： M. G. Calkin 著
出 版 社： Penguin
出版时间： 1996-12-1字数：版次： 1页数： 215印刷时间： 1996/09/01开本：印次：纸张： 胶版纸I S B N ： 9789810226725包装： 精装内容简介
This book takes the student from the Newtonian mechanics typically taught in the first and the second year to the areas of recent research. The discussion of topics such as invariance, Hamiltonian朖acobi theory, and action-angle variables is especially complete; the last includes a discussion of the Hannay angle, not found in other texts. The final chapter is an introduction to the dynamics of nonlinear nondissipative systems. Connections with other areas of physics which the student is likely to be studying at the same time, such as electromagnetism and quantum mechanics, are made where possible. There is thus a discussion of electromagnetic field momentum and mechanical "hidden" momentum in the quasi-static interaction of an electric charge and a magnet. This discussion, among other things explains the "(e/c)A" term in the canonical momentum of a charged particle in an electromagnetic field. There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton朖acobi equation of mechanics, the eikonal equation of optics, and the Schr鰀inger equation of quantum mechanics.
目录
Preface
CHAPTER I NEWTON'S LAWS
Newton's laws
Free fall
Simple harmonic oscillator
Central force
Gravitational force: qualitative
Gravitational force: quantitative
Parameters of earth's orbit
Scattering
Coulomb scattering
Exercises
CHAPTER II THE PRINCIPLE OF VIRTUAL WORK AND D'ALEMBERT'S PRINCIPLE
Constraints
Principle of virtual work
D' Alembert's principle and generalized coordinate
Lever
Inclined plane
Plane pendulum
Exercises
CHAPTER III LAGRANGE'S EQUATIONS
Lagrange's equations
Plane pendulum
Spherical pendulum
Electromagnetic interaction
Interaction of an electric charge and a magnet
Exercises
CHAPTER IV THE PRINCIPLE OF STATIONARY ACTION OR HAMILTON' S PRINCIPLE
Principle of stationary action
Calculus of variations
Geodesics
Examples
Path integral formulation of quantum mechanics
Exercises
CHAPTER V INVARIANCE TRANSFORMATIONS AND CONSTANTS OF THE MOTION
Invarianee transformations
Free particle (a)
Infinitesimal transformations
Free particle (b)
Space time transformations
Spatial displacement
Spatial rotation
Galilean transformation
Time displacement
Covariance, invariance, and the action
Exercises
CHAPTER VI HAMILTON'S EQUATIONS
Hamilton's equations
Plane pendulum
Spherical pendulum
Rotating pendulum
Electromagnetic interaction
Poisson brackets
Exercises
CHAPTER VII CANONICAL TRANSFORMATIONS
One degree of freedom
Gerrating functions
……
CHAPTER VIII HAMILTON-JACOBI THEORY
CHAPTER IX ACTION-ANGLE VARIABLES
CHAPTER X NON-INTEGRABLE SYSTEMS
INDEX
