Prerequisites for Arnold's Methods of Classical Mechanics

And I think that it is more difficult to understand physics and it is for mathematicians. In summary, the conversation discusses different books on classical mechanics and their mathematical complexity. The participants recommend Arnold and Landau as good choices for a more challenging read, while also mentioning other books such as Sommerfeld, Goldstein, and Lanczos. They also discuss the importance of differential geometry in classical mechanics and suggest learning it through books like Cartan and Flanders. The conversation highlights that Arnold's book may be more appealing to mathematicians due to its mathematical approach.
  • #1
etotheipi
I've finished with Gregory's classical mechanics and was looking for something a bit more challenging. I thought Arnold's methods of classical mechanics look pretty interesting, but it's definitely more mathematically complex than anything I would have done before, especially the bits about manifolds and differential forms - which I know essentially nothing about.

Do you think I'd be able to get anything out of it, or is the mathematical background required just too immense for now? Some other good choices might be Sommerfeld, Landau or Goldstein, which are maybe more physicsy. I wondered if anyone had some good advice... thanks!
 
  • Like
Likes PhDeezNutz
Physics news on Phys.org
  • #2
Arnold's classical mechanics is very mathematical, but a great introduction to the subjects you mention. I think you can never go wrong with Sommerfeld and Landau/Lifshitz. Goldstein has to be read with a grain of salt, particularly concerning the issue of nonholonomous constraints (if I remember right, the treatment using d'Alembert's principle is correct but the treatment with Hamilton's principle is wrong; it's correct in Landau+Lifshitz vol. 1).
 
  • Like
Likes etotheipi
  • #3
Arnold is great if you want an introduction to differential geometry, But I recommend first an intermediate course in mechanics.

Looking at gregory's book's table of content, I think canonical transformation and the Hamilton-Jacobi theory are missing.

So, if you are really (really) interested in the specific differential geometry stuff applied to mechanics, go for Arnold. Otherwise, differential geometry methods can wait until you know more stuff about analytical mechanics.
 
  • Like
Likes etotheipi and vanhees71
  • #4
Awesome, thanks. I think Landau has a section on the canonical equations, so in that case I'll attempt Landau before Arnold. That will probably take a little while, but should be good preparation 😊
 
  • Like
Likes vanhees71
  • #5
18-years-old are you already know the word "manifold"... wow.

Btw, being an engineer with 0 background in the subject I highly recommend Lanczos "The variational principles of mechanics". Pretty underrated book in my opinion, but one of the best I've ever read.

Landau I don't like because it does not indulge much in explanations: you understand ? good. you don't ? good. But it is a great book nonetheless. Lanczos on the other hand spends lots of time explaining even"trivial" stuff and I particularly enjoy the way he writes. Plus it is a very cheap book (Dover) which is always a pro. It also stresses the importance between differential geometry and classical mechanics several times throughout the book, but without getting too technical.

PS: probably I find Landau too hard because of my background, but you seem far more skilled than I am so you won't have any problem.
 
Last edited:
  • Like
Likes PhDeezNutz
  • #6
dRic2 said:
you already know the word "manifold"

I know the name... but I wouldn't say I know what it means, or any of the mathematics that describes them 😅

dRic2 said:
Btw, being an engineer with 0 background in the subject I highly recommend Lanczos "The variational principles of mechanics". Pretty underrated book in my opinion, but one of the best I've ever read.

Landau I don't like because it does not indulge much in explanations: you understand ? good. you don't ? good. But it is a great book nonetheless. Lanczos on the other hand spends lots of time explaining even"trivial" stuff and I particularly enjoy the way he writes. Plus it is a very cheap book (Dover) which is always a pro. It also stress the importance between differential geometry and classical mechanics several times throughout the book, but without getting too technical.

I did see that book recommended somewhere! I already started Landau yesterday so I think I'm going to try and stick with that, but I can pick up a copy of Lanczos probably next week to see if I like that also. Thanks!
 
  • Like
Likes vanhees71
  • #7
etotheipi said:
I know the name... but I wouldn't say I know what it means, or any of the mathematics that describes them 😅
Still impressive. At that age I wasn't even aware of the existence of integrals...

etotheipi said:
I did see that book recommended somewhere!
Probably it was me answering an other "book to learn analytical mechanics"-type post... I just copy-paste the same answer every now and then 😆😆
 
  • Like
Likes vanhees71
  • #8
I read some of Arnold when I started learning symplectic/contact geometry to get some physical intuition for the subject. It was definitely useful for that purpose, but maybe the fact that math people like the book isn't always the greatest advertisement for a physics text...
 
  • Like
Likes arturwojciechowicz, dextercioby and (deleted member)
  • #9
Infrared said:
I read some of Arnold when I started learning symplectic/contact geometry to get some physical intuition for the subject. It was definitely useful for that purpose, but maybe the fact that math people like the book isn't always the greatest advertisement for a physics text...

I would say it's actually a good book for physicists, I didn't find it as daunting as I thought. Unlike Abraham and Marsden, that book still give me nightmares.
 
  • #10
Arnold's Mathematical Methods of Classical Mechanics is very good book and introduction, worth to look at is also Ralph Abraham Classical Mechanics but all these books make sense with connection with Henri Cartan , H.Flanders - differential forms.
 
  • Like
Likes Ishika_96_sparkles and vanhees71
  • #11
Infrared said:
I read some of Arnold when I started learning symplectic/contact geometry to get some physical intuition for the subject. It was definitely useful for that purpose, but maybe the fact that math people like the book isn't always the greatest advertisement for a physics text...
May be it's true. Spivak is very mathematical.
 
  • #12
Arnold really can be read in your first year of university. It would be a mistake to avoid this book, alongside other less sophisticated treatments of mechanics.

I have been asked on some occasions to say something about differential forms. A symbol like '⨛f' is the 'same' but 'more advanced' as '∫f'

⨛f being the upper Riemann integral
 
  • Like
Likes vanhees71

Related to Prerequisites for Arnold's Methods of Classical Mechanics

1. What are the prerequisites for Arnold's Methods of Classical Mechanics?

The prerequisites for Arnold's Methods of Classical Mechanics include a solid understanding of calculus, linear algebra, and differential equations. It is also recommended to have some background in physics and classical mechanics.

2. Can I take Arnold's Methods of Classical Mechanics without meeting all the prerequisites?

While it is possible to take the course without meeting all the prerequisites, it may be challenging to fully grasp the material without a strong foundation in calculus, linear algebra, and differential equations. It is recommended to review and strengthen your knowledge in these areas before enrolling in the course.

3. Are there any online resources available to help me meet the prerequisites for Arnold's Methods of Classical Mechanics?

Yes, there are many online resources available to help you strengthen your understanding of calculus, linear algebra, and differential equations. Websites like Khan Academy, Coursera, and MIT OpenCourseWare offer free courses and tutorials on these subjects.

4. How can I assess if I meet the prerequisites for Arnold's Methods of Classical Mechanics?

You can assess if you meet the prerequisites for Arnold's Methods of Classical Mechanics by reviewing the course syllabus and checking if you have a good understanding of the topics covered. You can also take practice tests or quizzes to gauge your knowledge in calculus, linear algebra, and differential equations.

5. What should I do if I am struggling with the prerequisites for Arnold's Methods of Classical Mechanics?

If you are struggling with the prerequisites for Arnold's Methods of Classical Mechanics, consider seeking help from a tutor, joining a study group, or enrolling in a refresher course. It is important to address any gaps in your knowledge before attempting the course to ensure your success.

Similar threads

  • Science and Math Textbooks
Replies
6
Views
1K
  • Science and Math Textbooks
Replies
20
Views
2K
  • Science and Math Textbooks
Replies
17
Views
2K
  • Science and Math Textbooks
Replies
16
Views
3K
  • Science and Math Textbooks
Replies
14
Views
2K
  • Science and Math Textbooks
Replies
33
Views
4K
  • Science and Math Textbooks
Replies
7
Views
4K
  • Science and Math Textbooks
Replies
1
Views
1K
  • Science and Math Textbooks
Replies
9
Views
896
Replies
5
Views
2K
Back
Top