Which Classical Mechanics book to get?

[ConfusedMonkey]

Hi all,

I am looking for a good introduction to classical mechanics. I have looked at some book recommendations online but I am having trouble choosing the right book for me. Right now, I know no physics, so I need to start from the very beginning which I think is classical mechanics. I am self studying so I asked a friend to borrow one of his textbooks from school and he gave me a book called Essential University Physics, but a lot of people online said that the book isn't good and that it doesn't go in depth into classical mechanics. My end goal is to be able to read papers on the arXiv. I know this is a very lofty goal, but it is one that I want to pursue.

Given this, what's the best rigorous classical mechanics book that will prepare me for the path I want to take? My math background is fairly strong (rigorous multi-variable calculus, group theory, etc)

 

[jedishrfu]

The two that come to mind are Marion's book and Goldstein' book on Classical Mechanics.

These won't necessarily give you the skills to read any archive paper just ones heavily weighted to Classical Mechanics.

 

[ConfusedMonkey]

I didn't mean to be able to read arXiv papers after just this book. I just mean that my ultimate goal after however many years of self-study is to be able to read arXiv papers and stay in touch with modern day research. I don't expect to reach this level until after I have a very, very good grasp of GR and QFT, which is a long way down the road.

 

[atyy]

You should start with any of the standard high school or introductory university physics texts, eg. Halliday and Resnick, Young, http://web.mit.edu/8.01t/www/coursedocs/current/guide.htm, ...

Then read Kleppner and Kolenkow

Then read something which talks about Lagrangians and Hamiltonian, eg. Landau and Lifshitz, Fetter and Walecka

 

[Daverz]

I suggest French's Newtonian Mechanics. It starts out gently but covers a good amount of classical mechanics, though it does not cover Lagrangian or Hamiltonian mechanics. There is a companion Vibrations and Waves book.

 

[smodak]

https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 - this will be perfect for you

https://www.amazon.com/dp/189138922X/?tag=pfamazon01-20

You could also look at https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Since you know group theory, another interesting book for you to look at will be https://www.amazon.com/dp/3319192000/?tag=pfamazon01-20

 

[Buffu]

https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 - this will be perfect for you

https://www.amazon.com/dp/189138922X/?tag=pfamazon01-20

You could also look at https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Since you know group theory, another interesting book for you to look at will be https://www.amazon.com/dp/3319192000/?tag=pfamazon01-20

Omg I did not know Michael Spivak has a book on Mechanics. I am surely living under a "rock" these days.

 

[dextercioby]

Yes, Spivak-s intention (and also his final result) was to write a book at a satisfactory mathematical level, but more leaned towards text explanation and analogies for physical models. From my PoV, his book fills the clear literature gap between the classical Arnold and Abraham/Marsden/Ratiu and the rest of the mechanics books which have (much) less emphasis on mathematical foundations.

 

[Demystifier]

Yes, Spivak-s intention (and also his final result) was to write a book at a satisfactory mathematical level, but more leaned towards text explanation and analogies for physical models. From my PoV, his book fills the clear literature gap between the classical Arnold and Abraham/Marsden/Ratiu and the rest of the mechanics books which have (much) less emphasis on mathematical foundations.

There is a lot of mathematically oriented books on classical mechanics. Here is the list of all such books I am aware:

Abraham & Marsden - Foundations of Mechanics

Marsden - Lectures on Mechanics

Marsden & Ratiu - Introduction to Mechanics and Symmetry

Arnold - Mathematical Methods of Classical Mechanics

Davis & Johns - Analytical Mechanics for Relativity and Quantum Mechanics
(the title is somewhat misleading)

Fasano & Marmi - Analytical Mechanics

Jose & Saletan - Classical Dynamics A Contemporary Approach

Lagrange - Analytical Dynamics

Lanczos - The Variational Principles of Mechanics

Meyer, Hall & Offin - Introduction to Hamiltonian Dynamical Systems and the N-body Problem

Pars - A Treatise on Analytical Dynamics

Santilli - Foundations of Theoretical Mechanics (2 vols)

Scheck - Mechanics From Newton's Laws to Deterministic Chaos

Spivak - Physics for Mathematicians - Mechanics 1

Sudarshan & Mukunda - Classical Dynamics A Modern Perspective

Whittaker - A Treatise on the Analytical Dynamics of Particles and Rigid Bodies

Woodhouse - Introduction to Analytical Dynamics

Yourgrau & Mandelstam - Variational Principles in Dynamics and Quantum Theory

There are also books on dynamical systems (not listed above), which should be distinguished from classical mechanics. The boundary between dynamical systems and mathematical classical mechanics is not sharp, yet the former is a branch of mathematics while the latter is a branch of physics studied from a mathematical perspective.