On the Hamiltonian and Lagrangian formulation of classical dynamics for particles with spin

Abstract

The classical mechanics of nonrelativistic particles is generalized by also considering the spin components as canonical variables. Poisson-brackets and canonical transformations are discussed. The Lagrangian equations of motion are given and it is shown how rotational invariance leads to well known conservation laws. The method is extended to many dimensional spins and to the classical description of particles with isopin.