Should I read Thornton's or Lanczos' for Analytical Mech?

[davidbenari]

Next semester I begin studying analytical mechanics. The book they use in class is Thornton and Marion "Classical Dynamics of Particles and Systems". I wanted to read something about this during the summer, and stumbled upon Lanczos' book " The Variational Principles of Mechanics".

Lanczos' book has great reviews and talk a lot about how it really makes you understand stuff. I was afraid that it might a little bit over my level though.

What do you suggest? Should I read the book used in class (Thornton) or should I have fun with Lanczos? Or should I read both, hehe?

https://www.amazon.com/dp/0486650677/?tag=pfamazon01-20

You can see those reviews for yourself by following the above link.

 

[shinobi20]

Are you grounded enough in basic mechanics? If yes, you can try An Introduction to Mechanics by Kleppner and Kolenkow. Basically, his text is a rigorous treatment of Newtonian Mechanics that you will also find in Thornton's text, but the downside in Thornton's book is that he messed everything what Marion (original author of Classical Dynamics book) wrote. Thornton just basically added useless information and removed some information that is quite vital in the understanding of Mechanics. Also, the one thing lacking in Kleppner is the topic in Lagrangian and Hamiltonian, which you can find in other text like Thornton, but there are other better texts out there. Taylor is good but verbose, Gregory is good but often give problems which are hard to visualize and not so applicable in real life. Do not try to attempt Goldstein as it is a graduate book, you will miss out minor but important details in elementary mechanics. So the point is, if you want to have a better education in Newtonian Mechanics, K&K is hard to beat. See for yourself.

 

[davidbenari]

Thanks!

Do you know anything about Lanczos ? His book has great reviews.

 

[verty]

Thanks!

Do you know anything about Lanczos ? His book has great reviews.

I see this in the preview of Lanczos:

We can restrict our mathematical experiment to such paths as are infinitely near to the actual path. A tentative path which differs from the actual path in arbitrary but still infinitesimal degree is called a "variation" of the actual path.

This has multiple problems. First, the "actual path" is what is to be determined, so surely what he calls the actual path should be called the tentative path. It's tentative until we know it is actual.

Secondly, in what way is an infinitesimally varied path tentative when it goes against geometrical insight for there to be such a path? We can imagine it to be a mathematical tool to pretend there are infinitesimally varying paths, but surely no one can think they are tentative paths for the motion.

Hope this helps.

PS. I think you should try reading T&M. Looking at the review thread here on PF.com, no one has anything too bad to say about it.

 

[davidbenari]

I think you should try reading T&M.

Yeah, besides I think it'll be of more use since that's the book my class will use.

 

[shinobi20]

Thanks!

Do you know anything about Lanczos ? His book has great reviews.

I've read Lanczos before and I think it is great for the mathematical tools and further understanding of the variational principles of mechanics, as what the title says. Although I suggest you to read that later on as a supplement for your understanding but you can also do it now given enough time.

 

[verty]

Yeah, besides I think it'll be of more use since that's the book my class will use.

Yes, and I'm thinking that many people here have used the book, so if anything is unclear there will almost certainly be knowledgeable people who can get you unstuck or tell you how they overcame those issues. So hopefully you have no trouble and find the road to be quite smooth.

I always like the feeling of reading a well-known book, having a question, searching and finding a bunch of answers to that specific question because many people have used the book. It's so much easier.

With regard to my comments about Lanczos and infinitesimals, I don't know how important infinitesimals still are in modern books. It may be that Lanczos is still popular because that is the traditional way. My knowledge is vague in this area but I wanted to point out that his book had language that I would consider to be problematic (for the reasons that I gave in the previous post).

And as I have said in this post and the previous, my recommendation to try reading T&M was because it is a well-known book about which I have not seen anything substantively negative written (in comparison to Goldstein for example). I just wanted to make that clearer.

Thank you.

 

[mpresic]

Lanczos The Variational Principles is a good book on Mechanics but it is more of a monograph than a textbook. Lanczos presents a smaller variety of application of mechanics at a deeper level of Mechanics than Marion and Thornton or Goldstein (these are intermediate and graduate level textbooks respectively). Interested readers should mostly consider Lanczos after a graduate level textbook like Goldstein. Marion and Thornton is an intermediate level textbook, with a presentation of many applications and it is a good preparation for Goldstein. I am unaware of any class that uses Lanczos as a textbook. Most professors are looking for a book with a wider variety of well-studied applications, like Kepler's problem, Rigid bodies, the harmonic oscillator with normal modes, etc. By the way I do not think anyone reads Lanczos for fun. I suspect you can have more fun with Marion and Thornton, Kleppner and Kolenkow, Symon, or at a more advanced level Goldstein. Another books that is seldom mentioned is Classical Mechanics by Greenwood.

 

[mpresic]

Corben and Stehle Classical Mechanics is a nice dover as well