Is the motivation for the action principle purely from empirical evidence, or theoretical arguments, or a mixture of the two? As I understand it, there was some empirical evidence from Fermat's observations in optics, i.e. that light follows the path of least time, notions of virtual work and Maupertius's studies of classical systems and his observations/assertion that the path of a classical system through configuration space is one of least distance. Are there any other motivating ideas and/or arguments for why the action principle should be used to derive physical equations of motion, other than just that it works?!