tailieunhanh - Lectures on Classical mechanics

Lectures on Classical mechanics has contents: From Newton's Laws to Langrange's equations, equations of motion, lagrangian's and noether, time translation, conserved quantities from symmetries, example problems, electrodynamics and relativistic lagrangians, relativistic particle in an electromagnetic field,.and other contents. | Lectures on Classical Mechanics by John C. Baez notes by Derek K. Wise Department of Mathematics University of California, Riverside LaTeXed by Blair Smith Department of Physics and Astronomy Louisiana State University 2005 i c 2005 John C. Baez & Derek K. Wise ii iii Preface These are notes for a mathematics graduate course on classical mechanics at . Riverside. I’ve taught this course three times recently. Twice I focused on the Hamiltonian approach. In 2005 I started with the Lagrangian approach, with a heavy emphasis on action principles, and derived the Hamiltonian approach from that. This approach seems more coherent. Derek Wise took beautiful handwritten notes on the 2005 course, which can be found on my website: Later, Blair Smith from Louisiana State University miraculously appeared and volunA teered to turn the notes into L TEX . While not yet the book I’d eventually like to write, the result may already be helpful for people interested in the mathematics of classical mechanics. A The chapters in this L TEX version are in the same order as the weekly lectures, but I’ve merged weeks together, and sometimes split them over chapter, to obtain a more textbook feel to these notes. For reference, the weekly lectures are outlined here. Week 1: (Mar. 28, 30, Apr. 1)—The Lagrangian approach to classical mechanics: deriving F = ma from the requirement that the particle’s path be a critical point of the action. The prehistory of the Lagrangian approach: D’Alembert’s “principle of least energy” in statics, Fermat’s “principle of least time” in optics, and how D’Alembert generalized his principle from statics to dynamics using the concept of “inertia force”. Week 2: (Apr. 4, 6, 8)—Deriving the Euler-Lagrange equations for a particle on an arbitrary manifold. Generalized momentum and force. Noether’s theorem on conserved quantities coming from symmetries. Examples of conserved quantities: energy, momentum and angular