Here is the Table of Contents from Hand-Finch (with the rough correspondence to specific sections of [Marion-Thornton] in parentheses):
1. LAGRANGIAN MECHANICS
(Ch.7.1-7.7 of [MT])
2. VARIATIONAL CALCULUS AND ITS APPLICATION TO MECHANICS
(Ch. 6 of [MT])
3. LINEAR OSCILLATORS
(Ch. 3 of [MT])
4. ONE-DIMENSIONAL SYSTEMS: CENTRAL FORCES AND THE KEPLER PROBLEM
Ch. 5 and 8 of [MT])
5. NOETHER'S THEOREM AND HAMILTONIAN MECHANICS
(Ch. 2.5 and 7.9 of [MT])
6. THEORETICAL MECHANICS: FROM CANONICAL TRANSFORMATIONS TO ACTION-ANGLE VARIABLES
(Ch. 7.10-7.13 of [MT])
7. ROTATING COORDINATE SYSTEMS
(Ch. 10 of [MT])
8. THE DYNAMICS OF RIGID BODIES
(Ch. 11 of [MT])
9. THE THEORY OF SMALL VIBRATIONS
(Ch. 12 of [MT])
10. APPROXIMATE SOLUTIONS TO NONANALYTIC PROBLEMS
(parts of Ch. 4 of [MT])
11. CHAOTIC DYNAMICS
(Ch. 4 of [MT])
12. SPECIAL RELATIVITY
(Ch. 14 of [MT])
This is pretty close to the layout of the course, with the following
exceptions:
We will proceed at the (approximate) speed of one Section per week. The
twelve main Sections listed above will be flanked by (1) a summary of some
basic physics and math concepts (at the level of Ch. 1 and 2 of [MT])
before we proceed to Section 1 of [HF], and (2) special topics
after we are done with the body of [HF].