Classical Mechanics and Lagrangian/Hamiltonian Formalism: A Quick Review

[Elwin.Martin]

I'm beginning a directed study in QFT this fall and my supervising instructor told me I'd need to know some basics of Lagrangian and Hamiltonian Mechanics before we began (he also told me I needed to go back and review Perturbation Theory) since I'd need to know the formalism I guess?

I've read through the first chapter of Goldstein and am working into the second chapter but he said the book might be "unnecessarily difficult" in places. He told me Ch 2 and Ch 7 from that book if I was going through it (well, he said Ch 8 but I think the libraries copy had a different edition). I know what a Lagrangian is and what a Hamiltonian is and a little bit about why Lagrangians are useful (how to get Newtonian equations from them etc) but nothing very deep.

Do you have an recommendations if I just need a brief but strong overview of the classical equations used? Should I just focus on Lagrange's equations first or would it be reasonable to work on both sets simultaneously? He probably wouldn't mind covering it himself too much but I'd like to have a firm grasp of how to use them still, so if it's not possible in four weeks time I'd still like some recommendations. He uses the Taylor book for the class he teaches in Mechanics but he said he didn't want me to go out and buy a book if myself or the library didn't have it. I do have access to a number of other popular books though (we do have a decent library).

I should give a little more specific background so you can direct me to appropriate resources. I'm an undergraduate Applied Math/Physics major at a small school and I've finished Calc I (Stewart-ish book), Calc II(Stewart-ish book), Calc III(Stewart-ish book), Differential Equations(Boyce and DiPrima) and Linear Algebra(Strang). I've completed Physics I-III(Haliday and Resnick) and have privately studied Quantum Mechanics(Griffith's Ch 1-5) with a professor at another university. I'm not very far along in Physics but he thinks we can work through the Ryder book with some effort.

Thank you in advanced for your help and for your time!

 

[vanhees71]

I think the most important point concerning the action principle (in both its Lagrangian and Hamiltonian formulation) is to understand the connection between symmetries and conservation laws (Noether's theorem). Unfortunately, I know only German textbooks on this. A good one is Scheck's textbook on classical mechanics. Perhaps that's also available in English.

 

[Elwin.Martin]

I think the most important point concerning the action principle (in both its Lagrangian and Hamiltonian formulation) is to understand the connection between symmetries and conservation laws (Noether's theorem). Unfortunately, I know only German textbooks on this. A good one is Scheck's textbook on classical mechanics. Perhaps that's also available in English.

Thank you for your suggestion, can you give me a full title or author's name (German should be okay, I can Google from there)?

I'll be sure to look over the topics you recommended too.

 

[jtbell]

I think any intermediate-level undergraduate mechanics book should have something about the Lagrangian and Hamiltonian formalisms. I first learned them in a second-year course that used a book by Fowles (now Fowles and Cassiday). Other common books which I haven't used personally are by Marion, and Symon. Your college's library should have at least one of them.

 

[mathfeel]

If you want a good conceptual understanding of the subject, try to google Susskin's video on classical mechanics on Youtube. He goes very slow since it is a class for "layman". It probably won't help you do homework problem, but he explains stuff.

For the purpose of QFT, you probably just need a good understanding of the Hamiltonian principle of least action.

 

[vanhees71]

Thank you for your suggestion, can you give me a full title or author's name (German should be okay, I can Google from there)?

I'll be sure to look over the topics you recommended too.

Indeed, the book is available in English:

Florian Scheck, Mechanics, Springer

http://www.springer.com/physics/cla...-6?cm_mmc=Google-_-Book Search-_-Springer-_-0

 

[WannabeNewton]

Do you happen to have or have access to a copy of Principles of Quantum Mechanics - Shankar? There is a chapter dedicated to a a quick yet thorough coverage of Lagrangian and Hamiltonian mechanics in this text that might be helpful. It goes over each formalism and talks about canonical transformations, Poisson brackets, and symmetries so it could make the other textbooks easier to use.

 

[Elwin.Martin]

Do you happen to have or have access to a copy of Principles of Quantum Mechanics - Shankar? There is a chapter dedicated to a a quick yet thorough coverage of Lagrangian and Hamiltonian mechanics in this text that might be helpful. It goes over each formalism and talks about canonical transformations, Poisson brackets, and symmetries so it could make the other textbooks easier to use.

I have Shankar in my bag right now and I'm going to start looking over it as soon as I'm finished eating (though maybe after I look over Marion).

At present, my collection of library books I'm surveying (I do not intend to do them all, I'm not crazy) include:
Shankar's QM
Marion's Dynamics of Particles
Goldstein's CM

I've been told that looking into the Feynman & Hibbs book may be of use (for learning path integral formulation...?) but I'm not trying to kill myself or anything.

Thanks for the suggestion, what in particular should I be looking for though? I read the first err 30 pages a few weeks ago to get a feel for the book and it seemed pretty well written (IMO) but I don't know if I should try to finish the mathematical introduction or what.

Thanks again!

 

[Elwin.Martin]

Indeed, the book is available in English:

Florian Scheck, Mechanics, Springer

http://www.springer.com/physics/cla...-6?cm_mmc=Google-_-Book Search-_-Springer-_-0

I'm not sure the book is really right for me, I did read the first chapter or so and I'm not sure I like it though I think you're probably right about it being a good book. I bookmarked it for later investigation but I think I'm too slow to go through it at the moment.

Thanks for the suggestion though.

 

[DrSuage]

I like Finch and Hand's analytical mechanics. try that