Classical Mechanics for Physics Graduate Students - Ernesto Corinaldesi - Bog

"… there is an abundance of interesting examples which serves as a pleasant antidote to the many abstract and abstruse articles and books on classical mechanics … The areas covered in the text are quite wide-ranging, from small oscillations, bifurcations and rigid bodies to Lagrangian, Hamiltonian and relativistic systems. There are also short chapters on perturbation and field theories."
Mathematical Reviews

This book is intended for first year physics graduate students who wish to learn about analytical mechanics. Lagrangians and Hamiltonians are extensively treated following chapters where particle motion, oscillations, coordinate systems, and rigid bodies are dealt with in far greater detail than in most undergraduate textbooks. Perturbation theory, relativistic mechanics, and two case studies of continuous systems are presented.
Each subject is approached at progressively higher levels of abstraction. Lagrangians and Hamiltonians are first presented in an inductive way, leading up to general proofs. Hamiltonian mechanics is expressed in Cartan's notation not too early; there is a self-contained account of the traditional formulation.
Numerous problems with detailed solutions are provided. Graduate students studying for the qualifying examination will find them very useful.