E-Book Overview
These are notes for a mathematics graduate course on classical mechanics. I've taught this course twice recently. The
rst time I focused on the Hamiltonian approach. This time I started with the Lagrangian approach, with a heavy emphasis on action principles, and derived the Hamiltonian approach from that. Derek Wise took notes.The chapters in this LATEX 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. - John C. Baez
E-Book Content
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. I’ve taught this course twice recently. The first time I focused on the Hamiltonian approach. This time I started with the Lagrangian approach, with a heavy emphasis on action principles, and derived the Hamiltonian approach from that. Derek Wise took notes. The chapters in this LATEX 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”.