In this work we make an exposition on the Newtonian dynamics of curvilinear motion. We begin by making a small retrospect on this question, starting from the moment when Descartes’ conception of inertial motion rendered it problematic, and passing almost at once to the study of the different Newtonian approaches to this issue. We present Newton’s initial treatments - yet governed by the Cartesian idea of “Centrifugal Endeavour” - where we nonetheless can already observe the subtlety of a mathematical reasoning based on the notions of infinitesimal calculus. Afterwards, we emphasize the seeming contribution of Robert Hooke’s thought to the Newtonian conception of curvilinear motion, accomplished most of all by epistolary dialogues, yet rare or reticent. We emphasize how, after this exchange, Newton abandoned the notion of the action of a centrifugal force producing a kind of dynamical equilibrium of motion, in favor of a new understanding of the problem as a basically out-of-equilibrium mechanical system. We end with Newtonian final conception of motion, already framed in its essential aspects in the tract named De Motu, and finally presented in his master work Mathematical Principles of Natural Philosophy. We particularly point Newton’s deduction of Kepler’s planetary laws of motion, which has become one of the highest achievements of human science.
history of mechanics; Newton; mechanical force
