The Motion of Solid Bodies
This chapter concerns the study of the motion of bodies in the century of the Enlightenment. In the first part I introduce arguments about the great contribution of this century to mechanics. I then present the use of the principle of (the conservation of) living forces espoused by two of the major protagonists of the period, Johann and Daniel Bernoulli. With the principle of living forces the problems of motion of constrained solid bodies that were not possible to study with Newtonian mechanics were addressed. Then I present the different ways in which the theoretical mechanics will in fact be structured, that is as vector mechanics and as analytical mechanics. In this presentation the conceptions of the two greatest mathematicians of the second half of the XVIII century, Leonhard Euler and Lagrange are evidenced. The chapter closes with a presentation of the study of machines by Lazare Carnot who had a very important impact in applied mechanics of the XIX century.