Mechanics after Goldstein?

biubiu

Hi all,

I like physics and I just finished Goldstein's mechanics. I don't know what my next step should be in terms of textbooks on mechanics. Also I am only a rising college sophomore, and the math I know doesn't exceed an average college sophomore too much. Does anyone have any advices as to where I should go next? Thanks so much.

Boston_Guy

Goldstein is already a graduate level text so I don't see going to another one since it'd be at the same level or less. What I'd recommend is a text like The Classical Theory of Fields, Fourth Edition: by E M Lifshitz , L D Landau or any other text on continuum mechanics.

Dickfore

There are other parts of Physics besides Classical Mechanics. Do you have an interest for a particular topic?

Vanadium 50

Did you work the problems in Goldstein? If you can't work the problems yet, going on is not going to be helpful, and if you have a sophomore level math background, I can't see how you can work the problems.

Can you, for example, show that the polhode rolls without slipping on the herpolhode in the invariable plane?

Darwin123

By mechanics, I hypothesize that you mean classical mechanics. If so, I suggest an even more comprehensive book on classical mechanics. The text from which I learned graduate level classical dynamics is:
"Classical Mechanics" 2nd ed. by Herbert Charles Corben and Phuli Stehle (Krieger Publishing Company, Original edition 1960 and Reprint 1974).
Of course, I will not claim that the second edition is any better than the other editions. I conjecture that any text by these authors would probably be as good.
This text covers most of the same material as Goldstein (G). However, it goes into it a little more general and a little more rigoruous than Goldstein.
Corben-Stele (CB) is more a physicist's book than an engineering book. It approaches the subject on a more abstract level. CB introduces some higher mathematics. In some ways, it is more an introduction to quantum mechanics. It concentrates on many mathematical procedures in classical mechanics that found a better home in quantum mechanics. So in a way, it is like an introduction to quantum mechanics in a classical physics format.
I hypothesize that you are more interested in mechanics from the standpoint of fundamental physics then practical engineering. If so, CB is your book. However, I don't recommend CB for civil engineers. Goldstein would be a good introductory text for Corben-Stehle. However, I suggest holding on to your copy of Goldstein. You may want to compare approaches at some point. CB is rigorous and uncompromising.
CB does not concentrate on application. However, I many of the topics may be useful in numerical simulation. The reason is that it is mathematically rigorous. It doesn't rely on physical intuition. Although it doesn't start out with advanced mathematics, you better know your introductory calculus very well if you want to read CB.
The Corben-Stele book goes into more detail than Goldstein regarding contact transformations, Euler angles and perturbation theory. CB has good problems to work out.

K^2

Seconded. The only way to push further in mechanics is to study classical fields, and Landau-Lifshitz text on the topic is a good one to use.

Ben Niehoff

You can also read Arnold for a more abstract look at classical mechanics in terms of hamiltonian flows on symplectic manifolds.

Boston_Guy

Then again I recommend reading The Variational Principles of Mecanics by Cornelius Lanczos, Dover Pub (1970). Its a great book.

I also just picked up Classical Mechanics bby Donald T. Greenwood, Dover Pub (1977). It looks very interesting so far. Its about Variational Principles, Lagranges Equations, Hamilton's Equations, Hamiltonian-Jacobi Theory, Canonical Transformations and an introduction to Relativity.

YAHA

I was wondering the same thing. I now have more math than a typical sophmore; however, I still find Goldstein dense.

MathematicalPhysicist

The next logical step after mastering Analytical Mechanics (Lagrange and Hamiltonian formalisms) is to proceed to Determinstic Chaos.

One good introduction is the textbook by Florian Schleck, google for it.
In Arnold's you need to master differential geometry and manifolds theory beforehand.