ABSTRACT
Like the Lagrangian, one can define another fundamental quantity, the Hamiltonian, associated with the evolution of a mechanical system. This chapter provides a brief description of the Hamiltonian formalism in classical mechanics that forms the basis for working in a phase space. Hamiltonian canonical equations of motion are derived in terms of the generalized coordinates and generalized or canonical momenta. Unlike Lagrange’s equations of motion which hold in the configuration space, Hamilton’s equations are a set of two coupled partial differential equations representing the motion of the system in the phase space. The chapter introduces Poisson brackets and reviews their main properties including recasting Hamiltonian equations in terms of the Poisson bracket. It discusses Liouville’s theorem and touches upon the subject of singular Lagrangians and gives an exposition to higher derivative classical systems.
