Foundations of Mechanics, Abraham and Marsden

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Discussion Overview

The discussion centers around the suitability of Abraham and Marsden's "Foundations of Mechanics" as a resource for learning Classical Mechanics, particularly in terms of its mathematical rigor versus its physical intuition. Participants explore the balance between mathematical concepts and physical understanding in the context of the book's content.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the book provides a good intuitive grasp of Classical Mechanics, suggesting it may be more mathematical than physics-oriented.
  • Another participant highlights the advanced mathematical prerequisites listed in the book, expressing concern that these may be too challenging for most high school and undergraduate students.
  • A third participant agrees with the concern regarding the book's accessibility for students without a strong mathematical background.
  • A different participant claims to possess the necessary mathematical background but notes a difference in the definition of manifolds presented in the book compared to their prior knowledge. They express a desire for more physics-related content to develop a solid intuition for Classical Mechanics.

Areas of Agreement / Disagreement

Participants generally express concern about the book's accessibility and its focus on mathematical rigor over physical intuition. However, there is no consensus on whether the book is ultimately suitable for learning Classical Mechanics, as opinions vary regarding the balance of content.

Contextual Notes

The discussion reveals varying levels of mathematical preparedness among participants, which may influence their perspectives on the book's suitability. There are also differing expectations regarding the integration of physical concepts with mathematical frameworks.

Who May Find This Useful

This discussion may be useful for students considering advanced texts in Classical Mechanics, particularly those with varying levels of mathematical background and those interested in the interplay between mathematics and physics in learning materials.

ForMyThunder
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Is Abraham and Marsden's Foundations of Mechanics a good book to learn Classical Mechanics? In other words, if I were to go through this book (which I believe is more mathematical than physics-related) would I have a good, intuitive grasp of Classical Mechanics?
 
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How much background in physics and mathematics do you have already?

According to the preview feature on amazon.com, the "Preliminaries" section includes topology, finite-dimensional Banach spaces, local differential calculus, manifolds and mappings, vector bundles, ...

That looks like a major stretch (to put it mildly) for the vast majority of high-school students in the USA, and even for the vast majority of undergraduate university students.
 
jtbell said:
That looks like a major stretch (to put it mildly) for the vast majority of high-school students in the USA, and even for the vast majority of undergraduate university students.

I agree completely.
 
I actually have the necessary mathematical requirements, although just skimming through the book, it seems they give a more general definition for manifolds than I am used to, requiring them to be locally homeomorphic to a Banach space rather than Euclidean space. Other than that the math doesn't seem like it would bother me. I am more interested in whether the topics in this book contains enough physics-related material; although symplectic geometry is motivated by classical mechanics, I want a more physical approach than mathematical, something that will give me a solid intuition on the subject of Classical Mechanics.
 

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