Mathematical Methods of Classical Mechanics by V.I. Arnol'd

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Discussion Overview

The discussion revolves around the book "Mathematical Methods of Classical Mechanics" by V.I. Arnol'd, focusing on its accessibility, content, and comparison with other texts like Goldstein's. Participants explore its suitability for students in physics and engineering, particularly regarding Lagrangian and Hamiltonian mechanics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants describe Arnol'd's text as beautiful and a significant addition to the literature on classical mechanics.
  • Others note that Arnol'd's book begins with the concept of affine space, suggesting it may be more challenging than Goldstein's work.
  • One participant argues that there is much more to classical mechanics than what is covered in Goldstein's text, suggesting Arnol'd's book provides additional insights.
  • A participant questions whether Arnol'd's book is suitable for someone without a strong background in advanced mechanics, seeking advice on whether to study Goldstein first.
  • Another participant recommends starting with Goldstein or Calkin before approaching Arnol'd, emphasizing that Arnol'd's book focuses on mathematical rigor rather than physical concepts.
  • Some participants express differing views on the purpose of Arnol'd's book, with one asserting it offers a unique conceptual perspective on mechanics rather than merely adding rigor.
  • There is a suggestion that Goldstein's text may be more aligned with preparing students for quantum mechanics, which some participants find noteworthy.

Areas of Agreement / Disagreement

Participants generally disagree on the accessibility of Arnol'd's book for students without prior knowledge of advanced mechanics. While some advocate for starting with Goldstein, others believe Arnol'd provides valuable insights that complement existing knowledge.

Contextual Notes

Participants express varying opinions on the prerequisites for understanding Arnol'd's text, highlighting the potential challenges posed by its mathematical approach compared to more traditional physics texts.

For those who have used this book

  • Total voters
    12
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This is one of the most beautiful mathematical physics texts out there.
 
this is the text which starts with the idea of an affine space.somewhat tough as compared to Goldstein.
 
If you think Herbert Goldstein wrote in 800 pages is last edition all there is to write about non-quantum mechanics, there you are for a big surprise. There are at least 800 pages more to write about, and 400 of them you can find in this gem-book which I whole-heartedly recommend for anyone doing graduate studies in physics.
 
Not sure if I'm supposed to start a new thread or ask this here...

I'm an engineering/physics student (senior undergrad) trying to self-study to get a better grounding in Lagrangian/Hamiltonian mechanics. Is this book accessible as a "mature" introduction to advanced mechanics, or is it more for people who already know the stuff and just want to frame it more mathematically? Put another way, am I better off working through something like Goldstein first and then coming to this book, or should I start with this book right away?
 
Definitely use something like Goldstein or Calkin first. You won't learn physics from Arnold's book, you'll just learn how to make the physics more mathematically rigorous. Personally I find the former to be much more important and interesting than the latter. Cheers.
 
^Yes Goldstein and Arnold complement each other quite well. I don't agree that the purpose of Arnold is to dress mechanics up with rigor. I think Arnold is uninterested in doing that. The book gives a different way of thinking conceptually about mechanics. Arnold has an interesting perspective. I would warn against becoming too enamoured with Arnolds approach as some readers do. It is not the one true way.

dextercioby said:
If you think Herbert Goldstein wrote in 800 pages is last edition all there is to write about non-quantum mechanics, there you are for a big surprise.
I actually think of Goldstein as a quantum mechanics book. It seems a bit more interested in laying a foundation for later study of quantum mechanics than doing classical mechanics for its own sake. Not that there is anything wrong with that.
 
lurflurf said:
I actually think of Goldstein as a quantum mechanics book.

Yes, exactly! It's like how think of Spivak's calculus actually being an algebraic geometry book.
Those textbook authors try to trick us!
 

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