Lagrange's concept of force

pp. 207-227

in: J. C. Boudri, What was mechanical about mechanics, Berlin, Springer, 2002

Abstract

Lagrange was not only the person who laid the analytic foundation for variational calculus, he was also willing to elaborate on the idea that the principle of least action could be the fundamental principle for all mechanics, including both statics and dynamics. In the 1750s he was enthusiastically hailed as the defender of this new approach to mechanics by Euler and Maupertuis. But in 1788 the same Lagrange wrote the classic work Méchanique analitique,² in which the principle of least action appears only as a derivative theorem, subordinated to the principle of virtual velocities. Thus Lagrange would seem to personify the transformation of the principle of least action from a teleological principle to a mathematical theorem.