Best Classical Mechanics book (not intro to mechanics)

[Levi Tate]

Hello folks. I am taking some courses next semester over at Wayne, one of which is a 500 level, graduate level difficulty mechanics course. It's the course typically taken at the 300 level. I was wondering if anybody knew of a great book for this course at this level. I have both Taylor and Douglas, and I was just wondering if anybody knew of a good book. I want to get a head start for next semester now that this one is over.

Thank you in advance

 

[Segala]

Dear Levi,
the undergraduate most standard reference seems to be Marion and Thornton's Classical dynamics of particles and systems. At a more advanced level, I think we have Landau's book from the Course of theoretical physics. Then (I can only suppose since it is far beyond my skills) you can try Arnold's Mathematical methods, which people tell is really hard.

On a personal note, I really appreciate Fowles and Cassiday's Analytical mechanics: clear and direct to the point.

Best regards.

 

[WannabeNewton]

Arnold can be difficult depending on what you mean by difficult. If you've never done analytical mechanics using smooth manifold theory before (or have never seen differential geometry period) then the material might be hard but the problems in the text are quite easy so it isn't difficult in that regard. Note that Arnold's text isn't about classical mechanics per say but the mathematical methods used in it (e.g. Lagrangian and Hamiltonian mechanics on symplectic manifolds).

If Levi has Taylor then Marion would be a waste because it is on the same level and IMO Taylor is much better than Marion.

Landau's classical mechanics is certainly good but the gold standard of classical mechanics texts at the level you seek is Goldstein.

 

[alissca123]

There are lots of great CM books out there. Besides Taylor and Gregory some of my favorites are

- Scheck - Mechanics: From Newton's Laws to Deterministic Chaos
https://www.amazon.com/dp/3540219250/?tag=pfamazon01-20
-Lanczos - The Variational Principles of Mechanics
https://www.amazon.com/dp/0486650677/?tag=pfamazon01-20
-Fowles - Analytical Mechanics
https://www.amazon.com/dp/0534494927/?tag=pfamazon01-20
- Greiner - Classical Mechanics 1&2
https://www.amazon.com/dp/0387955860/?tag=pfamazon01-20
https://www.amazon.com/dp/3642034330/?tag=pfamazon01-20

* Also, Landau is not more advanced than any of the above

If these are not advanced enough, take a look at Classical Dynamics: A Contemporary Approach
by José & Saletan.
https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20
or Goldstein

 

[Levi Tate]

My brother has analytical mechanics by Fowles.

So many options!

Do you guys think it would be a good idea to do this.

I want to be as prepared as possible for classical mechanics, because at Wayne State University, they teach it at the graduate level. They've used Fowles, Taylor, and Gregory in the past, among others.

I want to learn the whole class over this summer so that when I take the class, it is all reinforcing the ideas of the course.

I used Taylor for intro to modern physics and I absolutely love his writing style, the only problem is that there are 50 problems from each chapter and I do not know which ones to do and which ones to skip. The Gregory book seems less rich in theory, but I have the solutions to every problem, so I figure if I do every problem in the first semester of the two semester course, 120 of them, and read this book, then I will be in a solid shape for next semester. (I get stressed out easily and I get really down on myself if I don't have a 4.0)

Do you guys think that is a good idea, to just use gregory because I have access to the solutions?

Also, is there a difference between analytical mechanics, does it introduce something earlier on, or focus on the mechanics of Lagrange and Hamilton?

 

[George Jones]

at Wayne State University, they teach it at the graduate level. They've used Fowles, Taylor, and Gregory in the past, among others.

These two statements are at odds with each other.

 

[Levi Tate]

Maybe they don't teach them at the graduate level compared to an advanced mechanics course, but they count for graduate credit, any 15 credits hour of them (500 and above physics classes) do for physics majors.

 

[Levi Tate]

I don't know. I just want to do good in the class.

 

[Segala]

Also, is there a difference between analytical mechanics, does it introduce something earlier on, or focus on the mechanics of Lagrange and Hamilton?

Dear Levi,
analytical mechanics (aka theoretical mechanics, classical mechanics, vectorial mechanics, and so on) is the description of non-relativistic and non-quantum mechanics through the tools of mathematical analysis. It has three main formulations: Newtonian, Hamiltonian, and Lagrangian; which differ in the way things are handled.

Newton worked before Hamilton and Lagrange, and both developed upon the elder's ideas. So, it is common practice to master Newtonian mechanics before tackling Lagrange's equations and Hamilton theory.

Best regards!

 

[jasonRF]

Working through almost any intermediate level mechanics book will be excellent "preparation" for the course you will be taking. If I were you I would pick one of the two that you own and just work through it, using the other to help shed light on things that you aren't clear on. I would pick the one that you like the best (that is, the one you think you can learn from the best). Having access to solutions for problems can be helpful for self studying - but I am guessing you can likely find solutions to some number of problems from any textbook online. I did a google search ("classical mechanics" taylor site:.edu) and the first two (non-pdf) hits provided the list of assigned problems and their solutions for courses. One was at SUNY Stony Brook:
http://max2.physics.sunysb.edu/~rastelli/PHY303.xhtml
The other at Maryland
http://www.physics.umd.edu/courses/Phys410/gates/
I'm sure there are many other sites as well since it is an often used text.


jason

 

[moogull]

Landau's classical mechanics is certainly good but the gold standard of classical mechanics texts at the level you seek is Goldstein.

Why not call it the "goldstein" standard!
... I must be bored.