Prosaic discussion of basic lagrangian field theory

[Sojourner01]

I'm currently trying to pre-familiarise myself with the course on lagrangian dynamics I'll be taking in the upcoming year, by reading the course notes supplied. I'm somewhat getting the hang of it, but I could really do with some more indepth discussion about the whys and wherefores. Could someone suggest a good introductory book with plenty of clear discussion? Problems and examples are secondary at this point, though of course if they make the reasoning clearer they're hunky dory. I've heard various people mention Goldstein; could someone give the full title to make it a little bit easier for me to find?

 

[robphy]

Some suggestions:

Mechanics (Landau / Lifshitz)
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20Introduction to Analytical Dynamics (Woodhouse)
https://www.amazon.com/dp/0198531982/?tag=pfamazon01-20

Lagrangian Interaction (Doughty) was enlightening
https://www.amazon.com/dp/0201416255/?tag=pfamazon01-20Structure and Interpretation of Classical Mechanics (Sussman / Wisdom) might also be enlightening
http://mitpress.mit.edu/SICM/

This looks like it might be fun:
http://www.authorhouse.com/BookStore/ItemDetail~bookid~32221.aspx
(I'll have to see if our library can get it.)

 

[Meir Achuz]

Put "Herbert Goldstein" into Amazon.com

 

[Shahin]

I think the Gantmajer´s book is one of the best, and it is, of course, of a russian guy.

 

[smallphi]

Many of the books mentioned above are classics or 'modern' but I doubt a beginner can pick up significant amount of understanding from them.

A good short book (only 109 pages and free download) that focuses on Lagrangians and Hamiltonians with amazingly succinct and straight to the point definitions (totally confusing in other books) with plenty of examples and exercises with answers is

Robert Dewar, Classical Mechanics:
http://freescience.info/go.php?pagename=books&id=1431

 

[Sojourner01]

Hmph, Dewar's work is fine right up until halfway down page 4. Like most other books I've seen, there's no explanation whatsoever of why the definitions given are the case.

"The condition for functional independence of the m constraints is that the rank of the matrix [whatever] must be its maximal possible value, m."

Why? If I knew the mathematics so well, I wouldn't need this book, would I?

 

[robphy]

Hmph, Dewar's work is fine right up until halfway down page 4. Like most other books I've seen, there's no explanation whatsoever of why the definitions given are the case.

"The condition for functional independence of the m constraints is that the rank of the matrix [whatever] must be its maximal possible value, m."

Why? If I knew the mathematics so well, I wouldn't need this book, would I?

I agree that Dewar's notes might be a little advanced...which might be expected of something concise. However, to be fair, the complete quote is:

"The condition for functional independence of the m constraints is that
there be m nontrivial solutions of eq. (1.3), i.e. that the rank of the matrix
$$\partial f_j({\mathbf q})/\partial q_i$$ be its maximal possible value, m."

where eq. (1.3) was
$$\sum_{i=1}^n \displaystyle\frac{\partial f_j({\mathbf q})}{\partial q_i} {\rm d}q_i \equiv \displaystyle\frac{\partial f_j({\mathbf q})}{\partial {\mathbf q}} {\rm d}{\mathbf q} =0$$

The use of the term rank was to help restate the main sentence with a little more mathematics. On a first or second pass, one could gloss over those finer mathematical details.
The Woodhouse text might be a little more your speed.
In it, he addresses what he has dubbed as the first and second "fundamental confusions of calculus".

Doughty's text also treats the more advanced "Lagrangian field theory", which you used in the title of this thread.

For something online, you might like:
Richard Fitzpatrick's Analytical Classical Dynamics: An intermediate level course
http://farside.ph.utexas.edu/teaching/336k/336k.html

 

[Sojourner01]

Thanks for your help, all. I think I'm sturggling here partly due to my fairly limited mathematical equipment - my department are fairly lazy when it comes to maths, so we get very little formalism. As an example, I don't have a clue where the discussion of matrices came from as it's never been introduced to me to use them in this kind of situation before. I find this negligence most frustrating, as it leaves me largely unable to pursue independent study since by necessity most books are very heavy on jargon, whereas my course is very light on it and thus I don't understand what they're talking about, even thugh the concept may actually be quite simple.

 

[robphy]

Maybe it's a good idea to invest in a good book on mathematical methods, like
Boas, Mathematical Methods in the Physical Sciences (3rd),
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

The now-cheaper 2nd edition is a less-pricey alternative:
https://www.amazon.com/dp/0471044091/?tag=pfamazon01-20

In my experience, lots of things first appear to come from thin air... Sometimes, you have to push your "I believe" button and move on. I think that it is very difficult to learn something "linearly", proceeding only when each step in a presentation is fully understood from start to finish. Hopefully, someday you'll see what was going on (by taking another course [on, possibly, a completely different topic] or by teaching it to someone or by reading on your own [following your own personal plan of study]).

 

[Dr Transport]

Try getting JB Marion,

http://search.barnesandnoble.com/BookSearch/isbnInquiry.asp?z=y&EAN=9780534408961&itm=1

I'd try to get the first or second edititon if you could.

There is a Schaum's outline in Lagrangian Dynamics as well as a Classical Mechanics Schaums

http://search.barnesandnoble.com/BookSearch/isbnInquiry.asp?z=y&EAN=9780070602328&itm=17

http://search.barnesandnoble.com/BookSearch/isbnInquiry.asp?z=y&EAN=9780070692589&itm=1

 

[Brad Barker]

heard good things about taylor's mechanics book:

https://www.amazon.com/dp/189138922X/?tag=pfamazon01-20

i'm working through landau and lifshiz myself, but it's a decidedly terse text.

 

[neutrino]

David Morin's lecture notes: http://www.people.fas.harvard.edu/~djmorin/textbook.htm
(I think it's chapter 5 of the 'Old Book')

David Tong
http://www.damtp.cam.ac.uk/user/tong/dynamics.htm