Classical Best analytical mechanics textbook recommandation

[TheCapacitor]

Hello,
I'm a second year physics student. We are going to use "hand and finch analytical mechanics", however the reviews I saw about this book are bad.
I've already taken calculus for mathematicians, linear algebra, classical mechanics, special relativity, and electromagnetism.

The topics it covers are:
Lagrangian Mechanics
Variational calculus and its application to mechanics
Linear Oscillations
One dimensional systems: Central forces and the kepler problem
Neother's theorem and Hamiltonian dynamics
Theoretical mechanics: From canonical transformations to angle-action variables
Rotating coordinates Systems
The dynamics of rigid bodies
And more.

Could you recommend the best book or study method you know?

Thanks

 

[dextercioby]

Shouldn't Goldstein still be the standard reference for a beyond first course on classical mechanics ?

 

[TheCapacitor]

I'll try Goldstein then

 

[bacte2013]

You might be interested in Landau/Lifshitz' "Mechanics" and V. Arnold's "Mathematical Methods in Classical Mechanics".

 

[smodak]

L&L and Arnold are very good but I also like the following
Analytical Mechanics by John Oliver
https://www.amazon.com/gp/product/0198766807/?tag=pfamazon01-20
toc here - https://global.oup.com/academic/pro...antum-mechanics-9780191001628?cc=us&lang=en&#

Another favorite of mine is (although I am not sure it covers all your topics)
Mechanics by Spivak
https://www.amazon.com/gp/product/0914098322/?tag=pfamazon01-20

Theoretical Mechanics of Particles and Continua by Fetter
is great as well.
https://www.amazon.com/dp/0486432610/?tag=pfamazon01-20

Speigel's book
has nice problems.
https://www.amazon.com/dp/0070843570/?tag=pfamazon01-20

and don't forget to read this beautiful book on the side
Emmy Noether's Wonderful Theorem by Neuenschwander
https://www.amazon.com/gp/product/0801896940/?tag=pfamazon01-20

 

[Frimus]

We are going to use "hand and finch analytical mechanics", however the reviews I saw about this book are bad.

It is funny to see how opinions of students on Hand's book differ from their teachers' views.

Petr Horava of UC Berkeley (mainly known for Horava–Lifshitz gravity) recommends Hand for his Analytical Mechanics course:
see http://www-theory.lbl.gov/~horava/105.html

The primary required text is L.N. Hand and J.D. Finch, "Analytical Mechanics":
"This book indeed reflects very closely the logic of Analytic Mechanics as I see it.
In my opinion, we are very lucky to have a really good book..."

"Goldstein is a classic text that is always a good book to have in your library. If you compare the Table of Contents of Golstein you will find that its logic is actually quite close to that of Hand-Finch. On the other hand, Goldstein was written in the 50's and it shows..."​

David Tong (University of Cambridge) in his "Lectures on Classical Dynamics" also recommends Hand as a primary text:
see http://www.damtp.cam.ac.uk/user/tong/dynamics/clas.pdf

"This very readable book covers everything in the course at the right level. It is similar to Goldstein’s book in its approach but with clearer explanations, albeit at the expense of less content."​

On the other hand, one needs to take into account that Berkeley and Cambridge are prestigious universities and the requirements laid on their students are high.

 

[vanhees71]

My favorite is Landau and Lifshitz vol. I. As all the books of this 10-volume series it comes right to the point.

Goldstein is generally a good book but utterly flawed on anholonomic constraints, describing the wrong vakonomic rather than the correct d'Alembert dynamics using a wrong implementation of the constraints (which are on the allowed variations/virtual displacements rather than on the generalized velocities).

Another good book, also containing "naive Newtonian mechanics" (i.e., the stuff one usually learns before using the variational principles) is

F. Scheck, Mechanics, Springer 2010

 

[ibkev]

I've noticed "Classical Dynamics: A Contemporary Approach" by José and Saletan, if often listed alongside Goldstein as a recommended reference for mechanics courses but I can't personally speak to it. Any thoughts for/against?