Introduction To Hamiltonian Mechanics

Abstract The power of Lagrangian mechanics has caused generations of students to wonder why it is necessary or even desirable, to recast mechanics in Hamiltonian form. The answer is that the Hamiltonian formulation is a much better base from which to build more advanced methods. The Hamilton equations have an elegant symmetry that the Lagrange equations lack. Another answer, not directly related to classical mechanics, is that the Hamiltonian function is used to write the Schroedinger equation of quantum mechanics. The differences between the Lagrange and Hamilton equations result mainly from the different variable sets in which they act. This chapter deals with phase space, Hamilton equations, example of the Hamilton equations, non-potential and constraint forces, reduced Hamiltonian, Poisson brackets, Schroedinger equation, and Ehrenfest theorem.