I need to practice Lagrangians and Hamiltonians...resources?

Geezer
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Joined: Fri May 16, 2008 1:27 am

I need to practice Lagrangians and Hamiltonians...resources?

Postby Geezer » Thu Sep 04, 2008 6:23 pm

It's been a while since I took classical mechanics, and I seriously need to brush up on Lagrangians and the classical Hamiltonian formalisms. Do you know of any good books or other resources that would give me a fair number of problems to practice (with solutions, of course, so I can see if I make mistakes)?

It's so easy to find practice problems for the lower-division physics stuff, but a tad challenging finding practice problems for upper-division mechanics...

Thanks in advance, y'all.
Geez

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Helio
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Joined: Thu Mar 15, 2007 7:11 pm

Re: I need to practice Lagrangians and Hamiltonians...resources?

Postby Helio » Fri Sep 05, 2008 4:35 am

Lagranian and Hamiltonian parts on the GRE are honestly a joke compared to same of the other stuff have asked... I know the practice inside out by now and the only thing you really need to know is the energy formulas and how you get a langranian or hamiltonian. actually finding something like frequency of small oscillations is not really on the test and if it is usually solvable without using 3 pages and langranians

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muonman
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Joined: Wed Aug 27, 2008 7:19 pm

Re: I need to practice Lagrangians and Hamiltonians...resources?

Postby muonman » Sat Sep 13, 2008 5:42 pm

I need to agree with Helio here. As a matter of fact, let me give you the 30 second Muonman's review of CLASSICAL Lagrangians and Hamiltonians for the PGRE:

L = T - V (where T = 1/2 mv^2)
H = T + V (where T = (p^2)/2m)

Lagrange's Equation of Motion (LEOM): dL/dq = d/dt (dL/dqdot)
Since the term on the left side of LEOM, (dL/dqdot) is the momentum (p), the right side must the time derivative of momentum. Thus if dL/dq = 0, then momentum is constant.

That's it. Memorize the factoids above and you're set. As a matter of fact, I challenge anyone to find a single classical Langrangian/Hamiltonian question on the practice PGREs that requires more than the above knowledge.




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