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I'm taking the second course in Classical Mechanics which is being taught from John R. Taylor's book Classical Mechanics. What I think seriously lacks in my course is the big picture; the course mostly focuses on problem solving and the course instructor, along with the textbook, seem to make no meaningful attempt to delineate in some quantitative detail the advantages (and disadvantages perhaps) of the Lagrangian (and Hamiltonian) formulation; where does everything come from mathematically (rather than just minimizing a functional in analogy with minimizing functions); discussions on symmetries, conservation laws etc.

I'd really like a text that gives someone not only the big picture but also the theoretical aspects of these two mathematical formulations of mechanics for an undergraduate. Recommendations?

I know of books by Chow, Mariona and Thorton, Morin and Taylor but all of them seem to take the problem solving approach rather than theortically analyzing the frameworks as well.

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  • $\begingroup$ In order of increasing mathematical sophistication, the books by: Goldstein (not the most modern), Jose and Saletan, V.I. Arnold, Spivak, Abraham and Marsden. The first is essentially a physics book, the second is kind of a bridge between the physics and modern mathematical treatment involving manifolds, and the last three are essentially math books. I've found it necessary to basically read parts of all of these and the books you mentioned to truly understand the pig picture and how it relates to modern mathematics. $\endgroup$
    – joshphysics
    Commented Oct 6, 2016 at 17:26
  • $\begingroup$ @joshphysics awesome. For the mean time, recommendations for someone who has ax courses in a term but would still like to make more headway with the material? What would be the best book to pick up now, before covering these in detail with time -- after undergraduate, during grad school etc. $\endgroup$
    – Junaid Aftab
    Commented Oct 6, 2016 at 17:28

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In addition to the reading suggestions made by @joshphysics, I encourage you to read Calkin's Lagrangian and Hamiltonian Mechanics, Fasano's Analytical Mechanics, Rasband's Dynamics and Whittaker's A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. My personal favorite is Rasband's book, because it is very short and deep.

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  • $\begingroup$ How would you rate/compare these books? For instance, skimming Calkin's book seems to give the impression that it contains the same standard material as in conventional books. $\endgroup$
    – Junaid Aftab
    Commented Oct 7, 2016 at 4:51
  • $\begingroup$ Calkin's book is pretty standard, but it emphasizes more in the conceptual framework of mechanics, and should help you get acquainted with the subject. I haven't read Taylor's book, but skimming through the table of contents gave me the impression that its a book more or less on the level of Marion's. Calkin's exposition is rather simple and not very formal, but he focuses almost only on Lagrangian and Hamiltonian mechanics, as opposed to most introductory textbooks. The book by Fasano is very formal (theorem-proof style), and Rasband's is advanced and intuitive, but sacrifices formality. $\endgroup$
    – gradStudent
    Commented Oct 7, 2016 at 6:57
  • $\begingroup$ Whittaker's text is constantly referenced by other authors, including Goldstein, Spivak and Abraham and Marsden. Another interesting book is the one written by Sommerfeld. I forgot to mention it, but Calkin's book includes action-angle variables and Noether's theorem (for both Lagrangian and Hamiltonian formalisms). $\endgroup$
    – gradStudent
    Commented Oct 7, 2016 at 7:02

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