Impact Theory: Formulation and Formalisation

Impact theory went through two decisive phases. The first was its formulation, due to Isaac Newton, who set it out in the Principia; the second, its formalization, by various mathematicians over a longer period of time. It was Newton certainly who gave the theory scientific status, as we currently understand this difficult and ambiguous expression. However, the preparation of the theory for use as a mathematical model, with all the resources of differential analysis, was due to other mathematicians.

The importance of Newton’s Philosophiæ naturalis principia mathematica (Mathematical Principles of Natural Philosophy) extends from the dynamics of rigid bodies to that of fluid bodies. Of the three Books making up the Principia, Newton devoted Book I to solids and Book II to liquids, although he used the same title for both, ‘The Motion of Bodies’, which allows us to conjecture that he considered solids and fluids as being subject to the same laws, in spite of the peculiarities of each. He made this explicit in the preface, where he explained what he understands by mechanics:

In this sense rational mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated. … [I] consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore I offer this work as the mathematical principles of philosophy, … and to this end the general propositions in the first and second Books directed.