Classical Mechanics Video 12 -- Hamiltonian Mechanics

This lecture is the second of a series of four on Hamiltonian mechanics. We start by applying the Legendre transform to the Lagrangian to show that it arrives at the Hamiltonian, and follow this up by obtaining Hamilton's equations of motion, which correspond to the Euler-Lagrange equation in Hamiltonian mechanics. We look at the physical significance of the Hamiltonian as the total energy of the system and show that it is conserved if the Hamiltonian has no explicit dependence on time. Finally, we do the Legendre transform for a simple mechanical system (object travelling horizontally at height h above the ground) to demonstrate how to obtain the Hamiltonian in cases where the Legendre transform needs to be used on actual Lagrangians.

Lecturer: Prof. Adam Micolich

Background: Yamashita Park, Yokohama Waterfront, Japan.