ABSTRACT
This chapter shows that the whole system of particles and fields is a mechanical system derivable from a Hamilton action principle. It starts by reviewing and generalizing the Lagrange-Hamilton principle for a single particle. In contrast with the Lagrangian differential equations of motion, which involve second derivatives, these Hamiltonian equations contain only first derivatives; they are called first-order equations. We are justified in completely omitting the last term on the right side of, despite its dependence on the variables r and t, because of its quadratic structure.
