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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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Spivak's Physics for Mathematicians, volume I: Mechanics sounds exactly like what you're after! – Alex Nelson Aug 21 '13 at 21:59

Try "Classical Dynamics", 5th edition by Stephen Thornton and Jerry B. Marion and you would not regret it.

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Welcome to Physics.SE! Book recommendation questions are limited here; please read our policy about it and expand your answer accordingly. – Emilio Pisanty Aug 21 '13 at 18:02

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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This book explicitly deals with differential geometry, which I would like to avoid. – R S Jan 9 '13 at 10:59
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. – gns-ank Jan 15 '13 at 13:13

If you are a mathematician the book, even though it is a bit old fashioned, "A treatise on analytical dynamics of particles and rigid bodies" by E.T. Whittaker, Cambridge University Press would be found useful.

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Mathematical Methods of Classical Mechanics by Vladimir Arnold. Off-topic, but also a very interesting read is his essay On teaching mathematics.

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