We will follow Hand-Finch pretty much linearly, at the speed of rougly one chapter per week, with some minor exceptions to be specified later. This will be preceded by two or three lectures on the mathematical language suitable for analytic mechanics, i.e., differential geometry. Here is the Table of Contents from Hand-Finch,
1. LAGRANGIAN MECHANICS
2. VARIATIONAL CALCULUS AND ITS APPLICATION TO MECHANICS
3. LINEAR OSCILLATORS
4. ONE-DIMENSIONAL SYSTEMS: CENTRAL FORCES AND THE KEPLER PROBLEM
5. NOETHER'S THEOREM AND HAMILTONIAN MECHANICS
6. THEORETICAL MECHANICS: FROM CANONICAL TRANSFORMATIONS TO ACTION-ANGLE VARIABLES
7. ROTATING COORDINATE SYSTEMS
8. THE DYNAMICS OF RIGID BODIES
9. THE THEORY OF SMALL VIBRATIONS
10. APPROXIMATE SOLUTIONS TO NONANALYTIC PROBLEMS
11. CHAOTIC DYNAMICS
12. SPECIAL RELATIVITY
This final chapter, on special relativity, is the only chapter which will not be covered in this course, for two reasons: First, it stands outside of the scope of this course, and secondly, it can be viewed merely as a specific application of the more universal, abstract formalism developed during the semester, to the special class of systems exhibiting Lorentz invariance.