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What is a good book for Analytical Mechanics?

To be more specific, I would prefer a book that:

  • Is written "for mathematicians", i.e. with high mathematics precision (for example, with less emphasis on obscure definitions such as "virtual displacements").
  • However, it must not assume graduate-level mathematics such as differential geometry.

Does this kind of thing exist?

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  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/111/2451 and physics.stackexchange.com/q/1601/2451 $\endgroup$
    – Qmechanic ♦
    Commented Jan 8, 2013 at 15:26
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    $\begingroup$ Spivak's Physics for Mathematicians, volume I: Mechanics sounds exactly like what you're after! $\endgroup$
    – Alex Nelson
    Commented Aug 21, 2013 at 21:59
  • $\begingroup$ Check out Schaum's Theory and Problems of Theoretical Mechanics. It might not do for a comprehensive book, but it certainly does not waste any time. $\endgroup$
    – Mikael Kuisma
    Commented Aug 12, 2016 at 21:42
  • $\begingroup$ If you really think that Landau & Lifshitz (LL) vol 1 'deals with diff. geometry' (as you say in a comment to aignas's answer), then no, the kind of book you are looking for doesn't exist. LL only use what used to be called 'advanced calculus', and it is not possible to do 'analytical mechanics' with less math than that. (Mind you, I would not recommend LL as a first book on analytical mechanics. OTH, Spivak's book mentioned above is excellent, though you'll have to stop with Lagrangian mech. if you really want to avoid diff. geometry, which does get used in the chapter on Hamiltonian mech.) $\endgroup$
    – linguisticturn
    Commented Jun 26, 2020 at 20:06

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Why not try Landau and Lifshitz Volume 1 on Classical Mechanics? It's a very good, short and dense text which is time tested and wonderfully written.

Ar do you want something different?

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  • $\begingroup$ This book explicitly deals with differential geometry, which I would like to avoid. $\endgroup$
    – R S
    Commented Jan 9, 2013 at 10:59
  • $\begingroup$ Well not all the chapters. However, you can skip the differential geometry bits and then come back later on, when you feel like doing differential geometry. This will be a very useful book in the future if you plan to study physics later on. $\endgroup$
    – aignas
    Commented Jan 15, 2013 at 13:13
  • $\begingroup$ @RS One can say many things about Landau and Lifshitz (LL), but that they write 'with high mathematics precision' (as the OP requests) is definitely not one of them. The tone is set in Eq. (4.3), where they write v^2 = (dl/dt)^2=(dl)^2/(dt)^2. I am not sure if this can be made mathematically precise even using hyperreal numbers. $\endgroup$
    – linguisticturn
    Commented Jun 26, 2020 at 13:12
  • $\begingroup$ More nontrivially, many derivations use non-obvious tricks that LL don't really justify or explain how general they are; you just sort of have to 'assimilate' such reasoning and, in time, hopefully become adept at it. A paradigmatic example of all that is their treatment of the Mathieu equation, (27.8). Finally, numerous moderately nonobvious statements are just asserted without explanation (a hallmark of LL). The LL texts are definitely a treasure trove of insight, but, IMHO, one that is best approached only after first learning much of the material elsewhere. $\endgroup$
    – linguisticturn
    Commented Jun 26, 2020 at 13:12
  • $\begingroup$ At the same time, if one really thinks that Landau and Lifshitz vol.1 'deals with differential geometry', then the answer to OP's question is that there simply isn't a book of the sort OP is asking for, nor could there ever be. (In fact, the mathematics in LL vol. 1 never goes beyond undergraduate mathematics: what used to be called 'advanced calculus', linear algebra, and differential equations, with a tiny bit of complex analysis.) $\endgroup$
    – linguisticturn
    Commented Jun 26, 2020 at 19:37

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