Physics Through Problem Solving XXIII: Classical Lagrangian and Hamiltonian

Ahmed Sayeed

University of Pune, Pune

In this article we shall discuss some problems where we find the Hamiltonian of a system starting from its from Lagrangian using Legendre transformation. We also discuss when the Hamiltonian can be taken as $H = T + V$, that is, as the sum of kinetic and potential energy functions, with no need for Legendre transformation.