Lectures on classical mechanics

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 Lagrangian and Newtonian Approaches......Page 8 Prehistory of the Lagrangian Approach......Page 12 The Principle of Minimum Energy......Page 13 D'Alembert's Principle and Lagrange's Equations......Page 14 The Principle of Least Time......Page 16 How D'Alembert and Others Got to the Truth......Page 18 The Euler-Lagrange Equations......Page 20 Lagrangian Dynamics......Page 22 Interpretation of Terms......Page 24 Time Translation......Page 26 Canonical and Generalized Coordinates......Page 27 Symmetry and Noether's Theorem......Page 28 Noether's Theorem......Page 29 Conserved Quantities from Symmetries......Page 30 Space Translation Symmetry......Page 31 Rotational Symmetry......Page 32 The Atwood Machine......Page 34 Disk Pulled by Falling Mass......Page 35 Free Particle in Special Relativity......Page 37 Gauge Symmetry and Relativistic Hamiltonian......Page 41 Relativistic Hamiltonian......Page 42 Relativistic Particle in an Electromagnetic Field......Page 43 Lagrangian for a String......Page 45 Alternate Lagrangian for Relativistic Electrodynamics......Page 47 The General Relativistic Particle......Page 49 Free Particle Lagrangian in GR......Page 50 Charged particle in EM Field in GR......Page 51 Jacobi and Least Time vs Least Action......Page 52 The Ubiquity of Geodesic Motion......Page 54 The Hamiltonian Approach......Page 57 Example: A Particle in a Riemannian Manifold with Potential V(q)......Page 60 Example: A Regular but not Strongly Regular Lagrangian......Page 61 Hamilton's Equations......Page 62 Hamilton and Euler-Lagrange......Page 63 Hamilton's Equations from the Principle of Least Action......Page 65 Wave Equations......Page 67 The Hamilton-Jacobi Equations......Page 70