Readings

Lagrangian and Hamiltonian classical mechanics, symmetries and conservation laws. Use of generalized coordinates to handle constraints to motion on surfaces or curves. Read the following parts of Goldstein to review and extend concepts you have already seen in Classical Mechanics II: pp. 34–45, 55–56, 61–63, 334–42, then 343–47 and 353–56 (i.e., specific parts of sections 2.1–2.3, 2.6, 2.7, 8.1, 8.2, and 8.5.) If you are feeling rusty with Classical Mechanics II material you might want to review sections 1–10 and 40 of Landau & Lifshitz.

On problem set 2 we will cover: D'Alembert's principle and systems with holonomic and non–holonomic constraints. Use of Lagrange multipliers to determine forces of constraint. If you want to read ahead the corresponding reading is Goldstein: Sections 1.3–1.6, 2.4, 2.5, and 8.5.

The main readings for Rigid Bodies are Goldstein chapter 4, sections 4.1, 4.2, 4.4, 4.6, and 4.9. (Note that 4.3 is a linear algebra review.) The chapter 4 reading is on rigid body kinematics where many physics topics will be familiar to you. Goldstein emphasizes vector notation and discusses rotations as matrices. Next read chapter 5, sections 5.1 and 5.3–5.7. Chapter 5 is on rigid body dynamics. We will not cover Poinsot's construction, so you may skip this material on pp. 201–205 of section 5.6. (Other sections from chapter 4 and chapter 5 may be of interest, but the above are the most important ones.)

If you find the reading in Goldstein too dense, you should consider reading Thornton & Marion chapter 11. I particularly recommend chapter 11, section 10 on the force–free motion of a symmetric top.

Our next item to discuss will be principal axes for oscillating motion. If you would like to read ahead, the reading for this will be Goldstein chapter 6 sections 6.1–6.4.

The reading for Canonical Transformations is Goldstein chapter 9, sections 9.1–9.7. (We will not discuss active infinitesimal canonical transformations with the same level of detail that Goldstein does in 9.6, but it is still good reading.)

The reading on the Hamilton–Jacobi equations and Action–Angle Variables is Goldstein chapter 10 sections 10.1–10.6 and 10.8. We will cover more examples of this material on problem set 6.

For Perturbation Theory the reading assignment is Goldstein chapter 12, sections 12.1–12.3.

Read Goldstein section 13.1 of chapter 13, on the transition from discrete to continuous systems.

For Fluids, read sections 8.6–8.10, 8.13, and 8.14 from the Mechanics book by Symon.

We have finished our discussion of fluids, but there is one final problem on this in Problem Set 9. Further reading on fluids, including lots of worked examples and plenty of problems, can be found in the book "A physical introduction to Fluid Mechanics" by Alexander Smits.

Read chapter 3 of Baker and Gollub on the Nonlinear Damped Forced Oscillator.

Read the sections from chapter 3 of Strogatz on Bifurcations.