Classical Mechanics Homework Assignment #16

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Classical Mechanics Homework Assignment #16, due by 9 am Friday December 2 to Krishna’s office Lab 2 3255.

  1. 13.5
  2. 13.10
  3. 13.12 (see Notes)
  4. 13.23 (see Notes)
  5. 13.26
  6. 13.33

Notes:

  • For 13.5, 13.10, 13.23, and 13.26, can you use the Hamiltonian H = T + U? Explain why or why not.
  • Problem 13.12 might look familiar to you. Do you recall where you saw it? _Why_ can’t we use the Hamiltonian H = T + U in this case? Of course the whole point of the problem is to show this explicitly, but you should make sure you understand why H can’t just be T + U in this case.
  • For 13.23, part (a) may be hard to show mathematically, but it should seem plausible given the physical situation. If you can’t figure out how to show part (a) mathematically relatively quickly, just use its results for the rest of the problem.
  • Problem 13.33 should be a good connection to your current work in MVC. We’ll use the divergence theorem (we’ll call it Gauss’s Law) extensively next quarter in E&M, so this problem is a nice preview of work to come.