Hamiltonian formalism and the state of a physical system

The purpose of this paper is to trace in a brief and readable manner, the e volution of mechanics from Newton to quantum mechanics. The key to the tran sition is the Hamiltonian formalism. We produce Hamilton's equations in spe cial cases to give some sense of the importance and intrinsic interest in t his formalism. Several examples are given to illustrate the power of the te chniques. The idea of the "state" of a physical system is discussed and con nections to quantum mechanics are made. (C) 2001 Elsevier Science Ltd. All rights reserved.