Historical context
The first systematic study of collisions was carried out by the Dutchman Christiaan Huygens (1629–1695) in 1668, presented to the Royal Society of London. Huygens discovered that in elastic collisions two quantities are conserved: momentum and “living force” (what we today call kinetic energy). His key insight was to analyse collisions from the point of view of a moving observer, anticipating by two centuries the concept of the centre-of-mass reference frame (Simonyi 2012, ch. 3).
Newton, in the Principia, generalised these discoveries by formulating the third law and the principle of conservation of momentum for isolated systems (Einstein and Infeld 1938, ch. 1).
The fact that in elastic collisions momentum and kinetic energy are conserved simultaneously is not a technical detail: it is what makes the problem solvable. Two independent conservation laws provide enough equations to determine the final velocities of both bodies. Huygens’s idea of viewing the collision from the frame in which the centre of mass is at rest — where everything becomes symmetric — is still today the most elegant trick for handling collisions.
For the full list of works cited: Riferimenti bibliografici.
Links
Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Urto elastico · Terza legge di Newton
Related exercises: Urto elastico tra due biglie · Vero o falso sugli urti · Dimostrazione urto elastico 1D