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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Answer
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
Differential Equations, Mechanics, and Computation by R. Palais
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
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