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I am a philosopher and I am seriously interested in learning classical mechanics. I would like a textbook, course or the like (with exercises) introducing the contemporary treatment of classical Newtonian mechanics. This means that I'm not interested in understanding classical mechanics as Newton himself understood it. I want instead the best contemporary reconstruction of Newton's theory. (That would mean, for instance, that infinite sum series have to be treated with the concept of limit, and not the way Newton did.)

However, I would like to avoid any reference to QM or Relativity, since in this moment I am more interested in having a pure understanding of Newton's theory than in learning Physics. In this respect, it would also be useful if I am pointed out to all the relevant chapters of a contemporary Physics textbook, even if that book does refer to QM or Relativity in the other chapters.

Another question would be, what kind of math concepts and skills do I need to master in order to pursue this study project? I suppose most concepts of calculus are among those. What others?

I hope someone can help me in this one.

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The standard modern texts on classical mechanics as it is currently understood are Abrahams and Marsden 'Foundations of Mechanics' Ralph Abraham and Jerrold E. Marsden, Publication Year: 2008 ISBN-10: 0-8218-4438-5 ISBN-13: 978-0-8218-4438-0 AMS Chelsea Publishing, vol. 364.H

and Arnold:

"Mathematical Methods of Classical Mechanics" (Graduate Texts in Mathematics, Vol. 60) 2nd Edition by V. I. Arnold (Author), A. Weinstein (Translator), K. Vogtmann (Translator)

Both require some knowledge of modern mathematics at the level of an undergraduate degree. The key ideas are the differential geometry of manifolds, including the calculus of differential forms. A good book for the latter, at the undergrad level, is "Differential Forms with Applications to the Physical Sciences" (Dover Books on Mathematics) by Harley Flanders. This at least is cheap at $16 or so.

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  • $\begingroup$ Thank you, @mikestone. I've found a free available version of the second edition of Foundations of Mechanics, published in 1987. Would that edition be enough? $\endgroup$
    – elmo
    Commented Sep 16, 2019 at 2:19
  • $\begingroup$ Abraham, Marsden, and Arnold are all accomplished mathematicians. This may have something to do with the fact that the Abraham-Marsden book takes more than 600 pages to get to the Kepler problem. Personally I am glad that I was not taught classical mechanics this way. Nevertheless, I agree that since the OP asked for a contemporary treatment, the references are appropriate. $\endgroup$
    – G. Smith
    Commented Sep 16, 2019 at 4:21
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There is no shortage of material for you to peruse in your quest. To be brief, what you are after would be a current freshman/sophomore physics course series that stops at electromagnetism & optics. These are generally taught at two different levels: one with calculus, for engineers and science majors, and one without, for non-majors. You want the one with calculus.

This means that to survive the experience, you'll need to be good at calculus. Learning calculus at the same time you are learning physics is a lot like learning about internal combustion at the same time you are rebuilding a blown engine in your car.

There are a number of different college textbooks whose most recent revisions would serve your needs adequately. My recommendation is for you to contact the university closest to you and look up the course offerings, find the appropriate ones per my description above, and determine which textboooks they will be taught from. Buy those and, if possible, arrange to audit the lectures or follow them on-line.

The pursuit of knowledge is the asking of many questions- good luck in your pursuit!

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  • $\begingroup$ Thank you, @nielsnielsen! $\endgroup$
    – elmo
    Commented Sep 16, 2019 at 2:07

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