Hamiltonian Mechanics in a Nutshell

Abstract

This chapter is an introduction to the basics of Hamiltonian mechanics, with an emphasis on its symplectic formulation. It thus motivates the symplectic techniques which will be developed in the forthcoming chapters. In fact, Hamiltonian mechanics is historically the main motivation for the study of the symplectic group in particular, and of symplectic geometry in general. For complements and an extended study the reader can consult with profit the treatises by Abraham–Marsden [2] and Arnol’d [3]; an elementary introduction at the undergraduate level is the classical book by Goldstein [63] and its re-editions. (This book is written for physicists, however, and the mathematics is not always rigorous.)