The Basic Formulation of Mechanics: Lagrangian and Hamiltonian Equations of Motion

The Lagrangian and Hamiltonian formalisms are among the most powerful ways to analyze dynamic systems. In this chapter we will introduce Lagrange’s equations of motion and discuss the transition from Lagrange’s to Hamilton’s equations. We write down the Lagrangian and Hamiltonian for a charged particle in an electromagnetic field, and introduce the Poisson bracket.