Question

Exactly how specifically can the Lagrangian be defined?

Answer 1

. Consider the system of a mass on the end of a spring. We can analyze this, of course, by using F = ma to write down m¨ x =−kx. The solutions to this equation are sinusoidal functions, as we well know. We can, however, figure things out by using another method which doesn’t explicitly use F = ma. In many (in fact, probably most) physical situations, this new method is far superior to using F = ma. You will soon discover this for yourself when you tackle the problems and exercises for this chapter. We will present our new method by first stating its rules (without any justification) and showing that they somehow end up magically giving the correct answer. We will then give the method proper justification.