拉格朗日及汉密尔敦力学LAGRANGIAN AND HAMILTONIAN MECHANICS

1996-12  

World Scientific Pub Co Inc  

Calkin, M.G.  

215  

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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.

PrefaceCHAPTER 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　ExercisesCHAPTER 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　ExercisesCHAPTER III LAGRANGE'S EQUATIONS　Lagrange's equations　Plane pendulum　Spherical pendulum　Electromagnetic interaction　Interaction of an electric charge and a magnet　ExercisesCHAPTER 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　ExercisesCHAPTER 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　ExercisesCHAPTER VI HAMILTON'S EQUATIONS　Hamilton's equations　Plane pendulum　Spherical pendulum　Rotating pendulum　Electromagnetic interaction　Poisson brackets　ExercisesCHAPTER VII CANONICAL TRANSFORMATIONS　One degree of freedom　Gerrating functions……CHAPTER VIII HAMILTON-JACOBI THEORYCHAPTER IX ACTION-ANGLE VARIABLESCHAPTER X NON-INTEGRABLE SYSTEMSINDEX

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