Best Textbooks for Hamiltonian/Lagrangian Classical Mechanics

[SeReNiTy]

I'm doing a project next semester on the hamiltonian/lagrangian formulation of classical mechanics and i was wondering what would be the best textbooks to learn from?

I've already studied some maths including calculus, calculus on manifolds, linear algebra, abstract algebra...

I was reccomended Classical Mechanics (Goldstein), what do you guys think?

 

[arildno]

Eeh, Goldstein, perhaps??
Alternatively, you might use Goldstein.

 

[dx]

Sommerfeld's Book is also a good reference.

 

[Brad Barker]

i found thornton and marion's book on the subject unreadable.

here's a telling example: during our coverage of scattering theory in my school's undergraduate classical mechanics class, the prof actually made print-outs from goldstein's text since it was far superior to T-n-M's.

i haven't read anything else from goldstein, but those few pages were very clear.

 

[Richie]

If you're only doing a "project" (a presentation, I'll assume), then you need something substantial, but to-the-point. In other words, you want something that'll teach you the entire Hamiltonian/Lagrangian formulation, in a nutshell. That's usually the most efficient way to gather information for a presentation/report.

With this in mind, I actually recommend...a quantum mechanics textbook! Chapter 2 of R. Shankar's "Principles of Quantum Mechanics" is devoted to a quick review of Hamiltonian/Lagrangian mechanics, and it contains all the basic concepts, principles and equations, in about 30 pages. It's condensed, but effective and efficient. So this is my recommendation.

Of course, if you want the most rigorous introduction known to man, then go ahead and use Goldstein. But since you're only giving a presentation, I'm guessing you want the Cliffs Notes version -- which can be found in Shankar's book.

 

[robphy]

What is it that you want to do in the subject..specifically?

Required reading: Feynman's "The Principle of Least Action" chapter in vol II of the Feynman Lectures. (Some interesting related introductions are here http://www.eftaylor.com/leastaction.html )

Do you want to do textbook problems?... Schaum's Outlines, Marion-Thornton, Landau-Lifshitz, Goldstein, Fetter-Walecka

Do want to prepare for QM and QFT?
For QM, yes... use a quantum text. For relativistic field theory, you might like Doughty's Lagrangian Interaction.
[advanced: Mackey]

Do you want to study foundations? (e.g. variational principles, geometrical structure)... Lanczos, [very advanced: Arnol'd, Abraham-Marsden, http://mitpress.mit.edu/SICM/ ]

A nice book [if you can find it] with a mix of geometrical foundations and problems is Woodhouse's Analytical Mechanics http://www.worldcatlibraries.org/wcpa/top3mset/463b7ef715179873a19afeb4da09e526.html

 

[SeReNiTy]

Essentially this "project" is just a unit where i can freely learn anything of my choice under the guidance of a professor. I've chosen to learn a proper formulation of classical mechanics with the intent to have a better understanding of the mathematical formulism (namely the lagragian/hamiltonian).

If time permits during the semester, i'll investigate the extension of these formulisms to quantum mechanics...

Btw, what is the difference between the second and third editions of goldstein's book?

 

[Richie]

Btw, what is the difference between the second and third editions of goldstein's book?

Ha! Practically nothing. The cover is different, that's about all. And the end-of-chapter exercises are rearranged to occur in different numerical order. You can even find errors in the latest edition! I get the suspicion that publishers don't want all the errors to be corrected, because then there can be no excuse for a new edition, and hence no new profits...

 

[Pyrrhus]

Check out Mechanics by Landau et al