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I'm looking for a textbook or online notes or a review article etc on a rigerous formulation of Lagrangian mechanics. I'm well aware of the book by Arnold but I would like something to accompany it. Perhaps something a bit more recent. There are a few things I would like it to have.

  1. At least as much differential geometry as Arnold. Even better would be a dedicated section on DG at the start to cover everything needed to read the book.

  2. It must use local coordinate systems and not try to do everything in a coordinate free way.

The book Foundations of Mechanics by Abraham and Marsden doesn't use local coordinates (and focuses on Hamiltonian mechanics more so than Lagrangian). The book by Spivak is nice too and but there's something about it that doesn't quite suit me.

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marked as duplicate by Qmechanic Oct 24 '15 at 15:21

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    $\begingroup$ I'm skeptical that there is a single book or set of notes which does all of the things you're describing in a self-contained manner. I have the books you've mentioned (along with Jose and Saletan), and I'd speculate that the best you can do is to read all perspectives and then create your own notes. You'll learn more this way anyway. $\endgroup$ – joshphysics Oct 19 '15 at 19:45
  • $\begingroup$ @joshphysics I have the book by Jose and Saletan as well actually, but while it's not what I'm looking for. You're probably right that I wont be able to find everything I'm looking for. In that case, do you know of any other references on this subject, even if they're not exactly what I want? $\endgroup$ – Okazaki Oct 19 '15 at 20:08
  • $\begingroup$ can't think of anything at the moment I'm sorry to say, but I'll update if something comes to me. $\endgroup$ – joshphysics Oct 21 '15 at 1:11
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I own 'Classical Mechanics' (5th) by Kibble and Berkshire, which begins formulation of Lagrangian mechanics very early and then introducing Hamiltonian mechanics later. I picked it up for about £20 and would definitely recommend for about that price.

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