Analytical mechanics book On my PHD I have to learn the following subject: Analysis on manifolds and Analytical mechanics. But my book is really not good to read; it is too hard. So I need some book that explains to me Lagrangian and Hamiltionian on manifolds, but to someone who doesn't know much phyics.
 A: From a mathematical perspective, the best introduction to the subject is probably V.I. Arnold's Mathematical Methods of Classical Mechanics, specifically chapters $3$ and $4$. Some find the text rather terse, but that may be a good thing if that is not your main area of study.
For more detail on the physics (though not on manifolds) you may want to consider the classic (no pun intended) text for physicists, which is Goldstein's Classical Mechanics.
A: What book to suggest really depends on your mathematical backround. A standard mathematical reference for this kind of thing is Foundations of Mechanics by Marsden. Also Geometry, Topology, and Physics by Nakahara is a nice book with some simple examples. You might also look at some of the lecture notes here http://www.gregnaber.com/
A: I was once myself searching for the same thing and I found this book:
Analytical Mechanics - Fasano
It seems pretty good, with plenty of examples and problems (most solved). I haven't had the chance to study it thoroughly but I hope it helps.
