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.