ABSTRACT
This chapter provides a general treatment of an action principle by taking recourse to variations which puts it in an elegant integral representation with the Lagrangian serving as the integrand between two terminal points of time. What the action principle says is that of all the possible paths, as the system traces out a trajectory from a given initial time t0 to a final time t1, the actual path, which is a solution of the equation of motion, is the one for which the action is an extremum. Interesting corollaries that follow from the action principle are the Lagrangian equations of motion and the Hamilton’s canonical equations of motion. The chapter considers the extended point transformations which are relevant for moving boundary problems and derives a particular variant of action principle. It briefly addresses the brachistochrone problem.
