拉格朗日及汉密尔敦力学LAGRANGIAN AND HAMILTONIAN MECHANICS
内容提要 ：
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 |
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