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I'm not looking for books which deal with the mathematical foundations of Newtonian mechanics. What I'm looking for are modern books which deal with conceptual foundations of Newtonian mechanics - by that I mean exact definition of force, inertia, frames of reference etc. It seems like much of the books that deal topics were written before the 80's or even older (like the one by Ernst Mach himself). And the people who seem to be bothered about these things today are mostly science educators, who again publish very little on these topics. I'm not looking for books written from a philosophical standpoint either. Something that'd be comprehensible by a undergrad would be just fine.

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Bernhard Heijstek
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3 Answers3

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You may have a look at the works of Noll and Truesdell, for example

Lectures on the foundations of continuum mechanics and thermodynamics

or at the paper of Eisenbud (which maybe has influenced implicitly many textbooks):

On the Classical Laws of Motion .

Note that this articles are written from completely different epistemological points of view.

I didn't read it yet, but this may be of interest, too: Classical Dynamics: A Contemporary Approach.

Some other references:

[Mechanical systems, classical models By P. P. Teodorescu][4]

[Differential Equations, Mechanics, and Computation by R. Palais][5]

Rational Mechanics by C.W.Kilmister

A first course in rational continuum mechanics by C. Truesdell

The elements of continuum mechanics by C. Truesdell

[Mathematical aspects of classical and celestial mechanics By V. Arnolʹd, V. Kozlov, A. Neĭshtadt][6]

[4]: https://books.google.com/books?id=k4H2AjWh9qQC&pg=PP3&dq=teodorescu+mechanics+volume+1&hl=en&ei=Z2g0Tr6JAZCr8AO6qfGgDg&sa=X&oi=book_result&ct=result#v=onepage&q=teodorescu mechanics volume 1&f=false [5]: http://www.amazon.com/Differential-Equations-Mechanics-Computation-Richard/dp/0821821385 [6]: https://books.google.com/books?id=25iQQvHe9awC&pg=PR6&dq=arnold+kozlov&hl=en&ei=MWo0TqjbE4a38gOqlL2hDg&sa=X&oi=book_result&ct=result#v=onepage&q=arnold kozlov&f=false

Glorfindel
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student
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Well, old question, but since I've came across it I'd like to leave a suggestion: Cornelius Lanczos, "The Variational Principles of Mechanics." This is (together with the book by Chandrasekhar) probably exactly what you are looking for. Another book by Lanczos, "Space Through the Ages" is also highly likely to contribute to your goals. Good reading!

user289216
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I really like

Also, Lagrange is pure genius; I'd say Lagrange's book is even better than Mach's; here's a translation of it:

Geremia
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