Classical Lagrangian and Hamiltonian mechanics

I liked "Classical Dynamics of Particles and Systems" by Marion and Thornton (advanced undergraduate classical mechanics)

 

Landau/Lifshits vol. 1 is great to. I'd not call it "easy going" however, but it's very worth to struggle through!

 

If you're just looking for an intro, nearly any senior-levle UG text will have what you want. The Marion/Thornton book is good. Fowles/Cassiday is also good. There are MANY to choose from. Go to your local university library (if there is one obviously) and just look through the books collected under "classical mechanics" or "analytical mechanics".

 

It's been a long time since I looked inside it, but I really liked Scheck. For the mathematically advanced reader (if you happen to know some differential geometry), the best choice is probably Arnold.

https://books.google.com/books?id=yUDo7VptDgIC
https://books.google.com/books?id=5OQlBQAAQBAJ

 

The first bits of Goldstein's book would probably be very beneficial.

 

I would start with David Tong's lecture notes on classical dynamics: http://www.damtp.cam.ac.uk/user/tong/dynamics.htm
They are free, so absolutely no harm in looking.

 

Anything but that, unless you like meaningless formulas and calculations. If you don't like meaningless formulas and calculations, maybe Arnold if you can handle it.

 

I second David Tong's notes. They are free after all. homeomorphic's recommendation of Arnold may be premature since you are asking for an "easy-going" introduction (the entire book is written from the perspective of differential geometry).

The book by Marion and Thornton is an established undergraduate classic. So is the book by Fowles and Cassiday, or the book by Taylor. They are suitable for senior-level classical mechanics courses.

 

I was recommending Arnold in the long term. For now, I'm just unrecommending Marion and Thornton. Unless, of course, ugly calculations and very little physical insight is your thing.

 

According to someone, every textbook is full of ugly calculations and very little physical insight lol. But yes, I understand. Arnold is a scary book. Have you run through it? I just finished the whole of Fowles/Cassiday and will be moving onto Goldstein soonish.

 

I think it's reasonably obvious to anyone who has read it that Marion and Thornton are not exactly Feynman when it comes to their physical insight. I have read most of Arnold, but the Appendixes get pretty wild, even for me (there's some good stuff in there if you ever want to understand differential geometry, though). But I have a PhD in math, so Arnold is kind of right up my alley. But I did start reading it in my first year of grad school, so it's not THAT bad. And I could have probably read it a bit earlier than that--as he says in the intro it's closer to a course for theoretical physicists than mathematicians.

One book I'd like to read when I get the chance that might possibly (can't say, since I haven't read it) fit the bill here is Spivak's Mechanics for Mathematicians book.

There's a free preview online.
http://www.math.uga.edu/~shifrin/Spivak_physics.pdf [Broken]

As you can see from the preview, it's not really that math-oriented, although maybe in the later chapters, it is. I haven't read the finished product. Anyway, it looks like Spivak wrote a book that is somewhat similar to one I was thinking about writing. So, I'll have to read it, and if I like it enough, maybe I won't have to write my own, but just refer people to Spivak and Arnold.

Lanczos also has a Classical Mechanics book that's somewhat interesting and a bit lower level.

 

I understand better now what you mean about M/T. Thank you.