What's the Next Step in Mechanics After Goldstein?

In summary: Then again, I recommend reading The Variational Principles of Mechanics by Cornelius Lanczos, Dover Pub. In summary, an expert recommends a text by Cornelius Lanczos for further study in mechanics.
  • #1
biubiu
12
0
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.
 
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  • #2
biubiu said:
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.

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 Lifgarbagez , L D Landau or any other text on continuum mechanics.
 
  • #3
There are other parts of Physics besides Classical Mechanics. Do you have an interest for a particular topic?
 
  • #4
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?
 
  • #5
biubiu said:
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.
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.
 
  • #6
Boston_Guy said:
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 Lifgarbagez , L D Landau or any other text on continuum mechanics.
Seconded. The only way to push further in mechanics is to study classical fields, and Landau-Lifgarbagez text on the topic is a good one to use.
 
  • #7
You can also read Arnold for a more abstract look at classical mechanics in terms of hamiltonian flows on symplectic manifolds.
 
  • #8
K^2 said:
Seconded. The only way to push further in mechanics is to study classical fields, and Landau-Lifgarbagez text on the topic is a good one to use.
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.
 
  • #9
Vanadium 50 said:
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?

I was wondering the same thing. I now have more math than a typical sophmore; however, I still find Goldstein dense.
 
  • #10
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.
 

1. What are some advanced topics in mechanics after Goldstein?

Some advanced topics in mechanics after Goldstein include Hamiltonian mechanics, Lagrangian mechanics, and nonholonomic mechanics.

2. How is Hamiltonian mechanics different from Lagrangian mechanics?

Hamiltonian mechanics is a reformulation of classical mechanics that uses the Hamiltonian function to describe the dynamics of a system, while Lagrangian mechanics uses the Lagrangian function. Hamiltonian mechanics is more general and can handle systems with constraints, while Lagrangian mechanics is more intuitive and easier to apply.

3. What is nonholonomic mechanics?

Nonholonomic mechanics is a branch of classical mechanics that deals with systems that have constraints that cannot be described by holonomic equations. These constraints are often related to rolling or sliding motions, and the equations for nonholonomic systems are more complex than those for holonomic systems.

4. How does statistical mechanics relate to mechanics after Goldstein?

Statistical mechanics is a branch of physics that uses statistical methods to study the behavior of large systems of particles. It is closely related to classical mechanics, and many concepts and techniques from mechanics after Goldstein are used in statistical mechanics.

5. Are there any real-world applications of mechanics after Goldstein?

Yes, mechanics after Goldstein has many real-world applications in fields such as physics, engineering, and robotics. For example, Hamiltonian mechanics is used in celestial mechanics to study the motion of planets and satellites, and Lagrangian mechanics is used in the design of control systems for robots.

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