Classical Mechanics III

Goldstein = Goldstein, Herbert, Charles P. Poole, and John Safko. Classical Mechanics . Pearson, 2013. ISBN: 9781292026558.

Landau & Lifshitz = Landau, L. D., and E. M. Lifshits. Mechanics . Addison–Wesley, 1960.

Smits = Smits, Alexander J. A Physical Introduction to Fluid Mechanics . John Wiley And Sons Ltd, 1999.

Strogatz = Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering . Westview Press, 1994. ISBN: 9780201543445.

Symon = Symon, Keith R. Mechanics . Addison–Wesley, 1971. ISBN: 9780201073928.

Thornton & Marion = Thornton, Stephen T., and Jerry B. Marion. Classical Dynamics of Particles and Systems . Cengage Learning, 2003. ISBN: 9780534408961.

Next up are Rigid Bodies which we’ll likely start at the end of this week and continue next week (they are not on problem set 2). The main readings for this entire topic are Goldstein chapter 4, sections 4.1, 4.2, 4.4, 4.6, and 4.9. Then read chapter 5, sections 5.1 and 5.3–5.7. 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. Chapter 5 is on rigid body dynamics. (Note that 4.3 is a linear algebra review. Other sections from chapter 4 and chapter 5 may be of interest, but the above are the most important ones.)

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 Oscillations is Goldstein chapter 6, sections 6.1–6.4.

We will spend a few weeks on our next subject: Canonical Transformations, the Hamilton–Jacobi equations, and Action–Angle Variables. The complete reading for this material is Goldstein chapter 9, sections 9.1–9.7 and then chapter 10, sections 10.1–10.6 and 10.8.

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.

After we finish discussing action angle variables our next subject will be Perturbation Theory, for which the reading is Goldstein chapter 12, sections 12.1–12.3.

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 with viscosity the readings are from Landau and Lifshitz, Fluid Mechanics, Chapter II, sections 15–17 and 19–20.

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

Read the sections from chapter 3 of Strogatz on Bifurcations.

Goldstein, Herbert, Charles P. Poole, and John Safko. Classical Mechanics . Pearson, 2013. ISBN: 9781292026558. Goldstein will serve as the main text for the majority of our material. However, we will also cover material that is not in Goldstein, in particular in our discussion of fluid dynamics and chaos. For the latter, there will be assigned readings from other sources.

Smits, Alexander J. A Physical Introduction to Fluid Mechanics . John Wiley And Sons Ltd, 1999

Symon, Keith R. Mechanics . Addison-Wesley, 1971. ISBN: 9780201073928. We will use a chapter from this book for reading material on non-viscous fluids.

Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering . Westview Press, 1994. ISBN: 9780201543445. An accessible yet detailed discussion of non-linear dynamics in both differential equations and iterated maps.

Landau, L. D., and E. M. Lifshits. Mechanics . Addison-Wesley, 1960. Used for Classical Mechanics II and hence useful here for review.

Thornton, Stephen T., and Jerry B. Marion. Classical Dynamics of Particles and Systems . Cengage Learning, 2003. ISBN: 9780534408961. A useful reference at a somewhat lower level than Goldstein, may be clearer for some topics.