Newtonian and Eulerian dynamical axioms. IV. The Eulerian dynamical equations

Abstract

In this fourth part of the series of articles [1-3], dedicated to the Newtonian and Eulerian dynamical exioms, special stress is put on Euler's dynamical equations governing the motion of any rigid body both free and subjected to arbitrary finite and infinitesimal constrains. In particular, the equations of motion of rigid rods are discussed. The paper contains a detailed analysis of D'Alembert's and Lagrange's dynamical philosophy, regarding "le corps proposé comme l'assemblage d'une infinité de corpuscules ou points massifs unis ensemble de manière qu'ils gardent toujours nécéssairement entre eux les memes distances", which displays clearly that such a hypothesis leads to a contradition with Newton's second dynamical law, namely "mutationem mous proportinalem esse vi motrici impressae et fieri secundum lineam rectam, qua vis ill imprimatur"