Opinions on 'The Variational Principles of Mechanics' by Cornelius Lanczos

MissSilvy

It was written by Cornelius Lanczos and from the reviews, seems to be a good book. I have completed two semesters of undergraduate classical mechanics using the Taylor and Thornton and Marion texts and I am looking for something that is not Goldstein mechanics. Is this a good stepping stone or is it best lest for grad mechanics and later? My math background is up to and including vector calculus, linear algebra, tensors, basic differential equations, special functions, and some experiences with Green's functions and Fourier transforms.

fluidistic

I was about to create a thread about almost the same question. Basically I've read most of the reviews from Amazon and this really looks a good book for the upper undergraduate level classical mechanics course. However I would like to know if it is appropriated as a textbook rather than a book that "only" teaches the history of classical mechanics.
Thank you.

Mike706

I haven't seen the book that you're referring to, but since you are just looking for a good mechanics book that is not Goldstein, the book by Landau/Lifshitz and the book by V. Arnold are definitely worth checking out. Landau is extremely concise (about 200 pages) and to the point, I liked it a lot. Landau is upper undergrad/beginning grad level. Arnold has a bit more math to it (see the table of contents) than Landau.

I haven't read Goldstein's book yet, but I have heard there are a few subjects meant as preparation for quantum mechanics (which I haven't studied, so I don't know the validity of this) in Goldstein's book that are not covered in Landau.

Landau
Arnold

If you haven't seen calculus of variations before, here is a good introduction to help with the first chapter of Landau, if you go that route:
MIT Calculus of Variations Video

mklejeune

For what it's worth, as someone with a copy of all the books mentioned so far (Landau, Lancsoz, Goldstein, Arnold) and still in the early stages of teaching himself the subject, I've opted to focus on completely digesting Mechanics by Landau/Lifshitz first. I find Lancsoz's book to be quite beautiful and inspiring actually, but the language for the time being appears geared towards someone that understands the subject better than I do at present.

Snicker

I love this book!

Lanczos is an amazing text and is something I would strongly recommend for its content, readability, and price. In my opinion, it is best used as a supplement for harder texts on classical mechanics such as Arnold, Whittaker, or Marsden*. This is because of the philosophical and intuitive based concepts in the book. Entire pages have not a single equation in them!

It provides a lot of interesting applications and theorems which, in modern literature, are unfortunately forgotten. It also has an amazing historical survey as an appendix.

Mathematically, the book is of medium level. Although it does go over the applications of Lie groups and Riemmann geometry (including a beautiful application of RG in Hamilton-Jacobi mechanics), the primary language Lanczos uses is analysis. This is in contrast to most 'modern' texts (Arnold, Marsden, Jose, Scheck, &c.) which is written in the language of abstract manifolds.

Overall, The Variational Principles of Mechanics is a gem and a definite recommendation if you don't mind plenty of philosophy and motivation.



*Both Introduction to Mechanics and Mechanics and Symmetry.

homeomorphic

I loathed Marion and Thornton with a passion. I remember I found Lanczos at the library and I sought refuge in it from Marion and Thornton. It wasn't quite the antidote to Marion and Thornton that I had hoped it would be from reading the introduction, but it did help. I was looking for more intuition and motivation and that seemed to be what Lanczos offered. And there was some, but not quite what I demanded.

I haven't read Goldstine, but from what I've heard, it actually sounds pretty good.

Arnold's book is one of my favorites, but I found that the later chapters of the book were the most insightful. The first chapter is really good because he motivates Newton's laws instead of just pulling them out of a hat, as the usual approach goes. But in the next few chapters, I think it's too close to the standard unenlightening approach, although there are definitely some nice highlights. You don't see how to think of the subject in a nice conceptual way until you get to the later chapters. So, it could be a good idea to skip ahead.

Baez has some good notes on CM:

http://math.ucr.edu/home/baez/classical/

There might be some hefty prerequisites to follow the whole thing, but I think you could understand a lot of it. It was written after I took classical mechanics, otherwise, I think it would have been the answer to many, but not all of my prayers. Certainly more of my prayers than Lanczos. Some of my prayers, I found I just had to answer myself.

There's also a nice overview in Penrose's Road to Reality.

AlephZero

I wouldn't call Lanczos "a textbook". If you just want to pass a course and tick another box on your study schedule, don't waste your time with it. But if you want a book that you can keep re-reading profitably for the next 40 or 50 years, buy it.