There are two primary reasons for using the principle of least action. First, it packages everything about a system in a very concise way. All the parameters (such as the masses and forces), and all the equations of motion are packaged in a single function—the Lagrangian. Once you know the Lagrangian, the only thing left to specify is the initial conditions. That’s really an advance: a single function summarizing the behavior of any number of degrees of freedom.
