Classical Mechanics Homework Assignment #16

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.

Week 9 Public Solutions associated due dates

Given the shorter turn-around time and other end-of-quarter exams and assignments, here are clear due dates for Week 9 Public Solutions:

  • See Public Solutions Guidelines for details.
  • due by 5 pm Fri. Dec. 2: typeset solutions saved to Workspace folder or narrative solutions links sent to Krishna via email, as detailed in the Guidelines.
  • due by 5 pm Fri. Dec. 9: Peer Reviews (see Guidelines for details) submitted to Author and to Krishna.
  • due by 9 am Mon. Dec. 12: Revised Solutions. Note: Revised Solutions are mandatory if a) you did not submit Revised Solutions to your Week 4 Public Solutions or b) if you received feedback that your Week 4 Public Solutions were substantively flawed. Otherwise, revisions are optional (though encouraged).

Week 9 Schedule Changes and Reminders

Please note the following changes and reminders for Week 9:

  • Mon. Nov. 28:
    • No changes to Multivariable & Vector Calculus: class still meets at 9 in Sem 2 D3105. Take-home exam due at 9 am (also complete Assessment Grid)
    • Krishna will be available for regular open hours in Sem 2 D3105 from 11 – 12:20.
    • Classical Mechanics meets at 12:30 in CAL West, not in Sem 2 D3105. We begin with a quiz on Chapter 9 material.
  • Tue. Nov. 29: No changes to regular schedule: Differential Equations still meets at 9 in Sem 2 D3105 and Classical Mechanics still meets at 12:30 in CAL West. DiffEq take-home exam available at end of DiffEq class meeting.
  • Wed. Nov. 30:
    • No changes to Multivariable & Vector Calculus: class still meets at 9 in Sem 2 D3105.
    • Seminar still meets at 11:30 in Sem 2 D3105. Bring 3 copies of your substantially completed Academic Statement for a peer review workshop. Copies should be double-spaced to leave room for reviewer comments. You can find previous Academic Statement Workshops here.
  • Thu. Dec. 1:
    • No Differential Equations class meeting.
    • INSTEAD, Classical Mechanics meets at 9 in Sem 2 D3105. We begin with a quiz on Chapter 11 material.
    • No class meeting Thu. afternoon.
  • Week 9 Public Solutions due by 5 pm Fri. Dec. 2. See Guidelines.

Lagrangians for CM HW#15

It is difficult to proceed with many of the HW#15 problems without the correct Lagrangian. The relevant Lagrangians are provided for intermediate self-checks here. It’s very important that you be able to write down Lagrangians correctly and apply small angle and small extension approximations appropriately. The Lagrangians have already had small angle and small extension approximations applied. They can (and should) be algebraically simplified further, but are left in the given form so it is easier to see the physical origin of each term, particularly the coupling term.

Classical Mechanics Homework Assignment #15

Classical Mechanics Homework Assignment #15, due by 5 pm Monday November 28 to Krishna’s office Lab 2 3255.

  1. 11.7
  2. 11.14
  3. 11.18
  4. 11.24
  5. 11.26
  6. 11.28

Notes:

  • For 11.7, any graphing application will do (Desmos, MMA, etc.).
  • Problem 11.28 might look familiar to you. Do you recall where you saw it?

Th. 11/17 workshop problems & teams:

Problem Team
11.14 Blake, Kian, Jake, Peyton
11.18 Emily, Leah, Pyxie, Time
11.24 Jeff, Isaac, Ky
11.26 Echo, Emily, Zane
11.28 Slade, Sheena, Vivian