Are There Scientific Errors in Goldstein's Classical Mechanics?

[Falgun]

So I am thinking of going through Goldstein's classical mechanics to learn the Lagrangian and Hamiltonian formalisms but am concerned because I've seen threads claiming that there are serious scientific errors in the book. I can't remember the specific thread. If so can someone recommend a resource which does not share the same flaws. I read a bit of Landau and understood the first few pages perfectly but it doesn't seem to have a lot of problems for practice and also it's rather slick. Any and all recommendations will be welcome.

 

[Frimus]

David Tong (free lecture notes)
Analytical Mechanics by Hand and Finch
Classical Mechanics by Gregory (AM basics)
Analytical Mechanics for Relativity and Quantum Mechanics by Johns

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[dextercioby]

Landau and Lifschitz for a cut to the chase approach (they teach you the essentials). For more text in front of your eyes, try Marion and Thornton. For full a mathematical approach, then V.I. Arnold's "Mathematical methods of mechanics" is the best.

 

[dextercioby]

And strict to Goldstein's treatment of D'Alembert's principle, @vanhees71 can assess where it goes wrong. BTW, virtual work and this approach is not fundamental (side material), and can be skipped. The concepts of variational principles, Lagrangians and Hamiltonians and connection between them are more important, since they are the basis of Quantum Field Theory.

 

[andresB]

goldstein 2nd edition is quite good in general, I would recomment it. just avoid te 3rd edition and everytin should be good.

 

[Vanadium 50]

If one of your textbook requirements is "no errors", or even "no bad spots", this cuts down the range. Perhaps to zero.

In the last year, you've wanted to self-study

• Upper Division Electromagnetism
• Differential geometry
• Probability and Statistics
• Real Analysis

Have you finished any of them? If not, what will be different this time?

 

[Falgun]

If one of your textbook requirements is "no errors", or even "no bad spots", this cuts down the range. Perhaps to zero.

In the last year, you've wanted to self-study

• Upper Division Electromagnetism
• Differential geometry
• Probability and Statistics
• Real Analysis

Have you finished any of them? If not, what will be different this time?

I did finish quite a bit of analysis and I ended up studying prob and stats at a bit lower level.Differential geometry gave me headache so I gave up on it. I read a couple of chapters of Purcell but then ran out of steam. I do plan on returning to all the stuff but I have time constraints cause I'm in the last year of my high school and I'm preparing for JEE (those who know will know). So basically I'm just trying my hand at stuff and see where it'll take me

 

[Falgun]

Landau and Lifschitz for a cut to the chase approach (they teach you the essentials). For more text in front of your eyes, try Marion and Thornton. For full a mathematical approach, then V.I. Arnold's "Mathematical methods of mechanics" is the best.

Lol I'm not sure I'm ready for Arnold.

 

[malawi_glenn]

Perhaps you want to try a simpler book first, like Taylor.
The book by Helliwell and Sahakian also touches upon quantization, looks promising.
Good short and cheap books are also the "A student's guide to" you have both one called "lagrangians and hamiltonians" and one called "analytical mechanics"

 

[apostolosdt]

As already mentioned, use 2nd edition. Attached is an errata list. Studying Chapter 12 is still a “must”.

 

[vanhees71]

And strict to Goldstein's treatment of D'Alembert's principle, @vanhees71 can assess where it goes wrong. BTW, virtual work and this approach is not fundamental (side material), and can be skipped. The concepts of variational principles, Lagrangians and Hamiltonians and connection between them are more important, since they are the basis of Quantum Field Theory.

It's a great unjustice of Goldstein's very good textbook that other people edit it later and make it wrong. The single-authored 2nd edition is the good version. I don't understand, why the authors didn't write their own textbook with their private theory to implement non-holonomic constraints in a wrong way...

I'd anyway rather suggest to read Landau and Lifshitz vol. 1, which is a much more economically written books on classical mechanics based on the action principle from the very beginning.

 

[Frabjous]

Given your background, I would recommend Marion, Taylor or the OOP Symon. L&L, Goldstein and Arnold are probably too advanced.

 

[MidgetDwarf]

I did finish quite a bit of analysis and I ended up studying prob and stats at a bit lower level.Differential geometry gave me headache so I gave up on it. I read a couple of chapters of Purcell but then ran out of steam. I do plan on returning to all the stuff but I have time constraints cause I'm in the last year of my high school and I'm preparing for JEE (those who know will know). So basically I'm just trying my hand at stuff and see where it'll take me

So you are a high school trying to read books that are used in strong undergraduate programs in the 3 to 4th year, and a book that is usually a standard for a graduate course?

I highly doubt 99% of high school students are able to read and work through the problems in these books.

At this point, it appears that you are wasting your time. Math/Physics books are not novels that can be read page by page, without getting hands dirty, and working through the exercises meticulously. Work upwards not topdown.

 

[Falgun]

So you are a high school trying to read books that are used in strong undergraduate programs in the 3 to 4th year, and a book that is usually a standard for a graduate course?

I highly doubt 99% of high school students are able to read and work through the problems in these books.

At this point, it appears that you are wasting your time. Math/Physics books are not novels that can be read page by page, without getting hands dirty, and working through the exercises meticulously. Work upwards not topdown.

Well people who prepare for physics Olympiad routinely solve problems from books like Purcell, Griffiths and Morin and grinding out probability and statistics from a math methods book is not impossible. If I encounter something which I clearly am not ready for like differential geometry I give up on it. Also I believe that I have math background for Goldstein (please correct me if I'm wrong) I've completed single variable and multivariable calculus and ODEs and linear algebra from MIT OCW. All I'm looking for is something challenging which my schoolwork is obviously not. I'll try my hand at Goldstein and let you know if I make any headway. Surely can't hurt to try? Right?

 

[vanhees71]

Just be sure to get the 2nd edition and avoid the 3rd edition.

 

[Frabjous]

Surely can't hurt to try? Right?

You have already hit the wall a couple of times. Use one of the easier books.

 

[malawi_glenn]

I've completed single variable and multivariable calculus and ODEs and linear algebra from MIT OCW

That basically says nothing on what you actually can.

If I encounter something which I clearly am not ready for like differential geometry I give up on it.

One should be ready for differential geometry if one has "completed" those courses you mentioned.

Surely can't hurt to try? Right?

It's your life and your free-time, you can do what you want with that. But you would be wasting your time on Goldstein at this point IMO.

Well people who prepare for physics Olympiad routinely solve problems from books like Purcell, Griffiths and Morin

Why don't you simply get and study Morin then? (or Taylor)
We often learn things in steps, you do not learn Lagrangian and Hamilotinans once and for all. You start with a basic book and work your way upwards. Like Morin/Taylor ->Goldstein/Landau -> Arnold

 

[vanhees71]

I think, it's always good to visit a library (or the internet ;-)) and look at different books. If you find one you think you can handle try it out for more thorough study. To know, whether you understand the content it's mandatory to solve the problems in the book. If you realize that the level of the book is too high, i.e., you cannot solve most of the problems after studying, try to figure out, what you don't understand and use a more introductory book.

 

[malawi_glenn]

I just think it way more efficient to study more introductory books first. If the problems are too easy, they don't feel like waste of time because doing basics is always good.

 

[MidgetDwarf]

Well people who prepare for physics Olympiad routinely solve problems from books like Purcell, Griffiths and Morin and grinding out probability and statistics from a math methods book is not impossible. If I encounter something which I clearly am not ready for like differential geometry I give up on it. Also I believe that I have math background for Goldstein (please correct me if I'm wrong) I've completed single variable and multivariable calculus and ODEs and linear algebra from MIT OCW. All I'm looking for is something challenging which my schoolwork is obviously not. I'll try my hand at Goldstein and let you know if I make any headway. Surely can't hurt to try? Right?

Yes, but often these students are looking at solution manual for every single problem. Which defeats the purpose of reading said "advanced" books. If you have completed calculus, ode, and linear algebra, you can learn the basics of differential geometry. So clearly your preparation is lacking in regards to these fundamental classes which are the cornerstone of math/physics. It is not a race to cram the material all at once. Only a selected few can do this, and those that can, are usually people who make grand contributions in the fields in which they choose to study.

Maybe go back and work through calculus, ode, linear algebra, and some 2nd year physics books thoroughly. Which would be using your time wisely.

Even tho I have a math degree, I still review the basics time and time again, while learning new material simultaneously.

Just yesterday, I was able to solve some group theory problems, without relying on powerful results, by changing the problem to a number theory problem. Something that was possible by me having reviewed number theory two months ago for a month. Repetition adds insights...

 

[Falgun]

Yes, but often these students are looking at solution manual for every single problem. Which defeats the purpose of reading said "advanced" books. If you have completed calculus, ode, and linear algebra, you can learn the basics of differential geometry. So clearly your preparation is lacking in regards to these fundamental classes which are the cornerstone of math/physics. It is not a race to cram the material all at once. Only a selected few can do this, and those that can, are usually people who make grand contributions in the fields in which they choose to study.

Maybe go back and work through calculus, ode, linear algebra, and some 2nd year physics books thoroughly. Which would be using your time wisely.

Even tho I have a math degree, I still review the basics time and time again, while learning new material simultaneously.

Just yesterday, I was able to solve some group theory problems, without relying on powerful results, by changing the problem to a number theory problem. Something that was possible by me having reviewed number theory two months ago for a month. Repetition adds insights...

I think that's good advice. Maybe I'll take a refresher using something higher level.