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Classical Mechanics II - Spring 2014

Welcome to Classical Mechanics II! This is not the official page for the whole course, but it will be official insofar as my role as the TA. I'll put up some supplementary resources that I've found useful in learning mechanics  as well as any other pertinent information. You should always feel free to contact me by email if there's something I can help you with or you have a question on physics — presumably related to mechanics but not necessarily!

The Lagrangian formalism is extremely powerful. While it may at first seem like a mere "second pass" on solving classical mechanics problems (just harder ones) it is much more. It represents a whole new way of approaching physics and is the basis of many advanced techniques, including field theory. I remember being awed once I realized its value, so I hope you have the same experience!



My office: Rm 357
Office hours: Tuesdays from 4:00 to 5:00 PM  /  Fridays from 4:30 to 5:30 PM
Recitation: Thursdays from 1:30 to 2:20 PM
Email: 

Homework Policy: DUE on Wednesday by 5pm. You can hand it in at your lecture or directly to me. My mailbox also works, which is in Rm 366 (admin office). Late homework will be assessed 10% of the total points per day. Unfortunately, I can't accept homework anytime after the section as I will often discuss the problems there. If there is an unavoidable obstacle preventing you from getting it in by the due date, please get in touch with me by email well in advance of the due date. Re-grades are sometimes possible; if you think it's warranted, please get in touch.  
Grades: The homework is just a small portion of your final grade. I would be less concerned about the numerical grade on the homework and focus more on making sure you understand everything. That's where I'm very happy to help. 



Problems covered in Section:
In section I'll point out some of the common missteps I saw on the homework (which I hope to have back to you every Thursday - no promises!) and discuss how to rectify them. With those in mind, I'll try to find a problem or two that are at once illuminating and interesting. If there is interest and time, we can work them out in section. Otherwise, I'll just post them here if I have any. 

The wave equation from the Lagrangian formalism and an example of chiral waves in spin-systems. This week the homework made us comfortable with the calculus of variations in an arbitrary number of dependent variables. What happens when you have more than one independent variable? The answer is simple, but the implications are pretty cool. Check out the attached for a simple example of a field theory -- that of a string. It takes on a new form when the problem of domain wall dynamics is cast as a field theory of a string. Research along those lines is happening here at Johns Hopkins. Check out the paper by Prof. Oleg Tchernyshyov and his student for more details. 

An example of coordinate-free proofs: Conservation of the Runge-Lenz vector. This week the homework helped us get comfortable with vector manipulations and working with non-inertial frames. One thing that helps in all of this is the powerful apparatus of thinking in a way that independent of any specific choice of coordinate system. The problem we tackled in section was a (perhaps intimidating) example of that. Here is my workup of the problem. The conserved quantity we deal with is known as the Laplace-Runge-Lenz vector. Keep it in mind as we come up to central force systems in a few weeks. Also, if you like quantum mechanics, you'd be interested to know that it forms the basis of an extremely elegant way of solving the Coulomb potential. Ask me if you're interested. 

Practice Exam Solution: Particle in a quadratic potential. Here you'll find solutions to a practice problem on central force motion and effective potentials. The problem was distributed by email and was on last year's exam. 


Helpful supplementary (NOT required!) texts:
*An asterisk means that I own a copy, so feel free to come look at mine if you can't find it at the library or want to "try before you buy". 
  1. *"Calculus of Variations," by Gelfand and Fomin: This short text covers variational calculus from start to finish with a good number of applications to physics. It has served me well as a reference when physics books don't quite cut it. Most of the text gets quite advanced, but the beginning chapters are very clear and spell out the foundations. If you like to see the machinery inside the black box, this will be a good book for you. 
  2. *"Classical Mechanics" by Goldstein: This is the standard graduate text in classical mechanics. It's very readable and if you're planning on graduate school it doesn't hurt you to have it now. Moreover, it's becoming less common to require a course in classical mechanics in graduate school so it doesn't hurt you to learn it in a bit more depth while you're at it. 
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Guy Marcus,
Feb 15, 2014, 8:46 AM
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Guy Marcus,
Apr 10, 2014, 1:42 PM
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Guy Marcus,
Feb 11, 2014, 1:50 PM
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