Concept
Vis viva (from the Latin for "living force") is a historical term used to describe a quantity similar to kinetic energy in an early formulation of the principle of conservation of energy. Proposed by Gottfried Leibniz over the period 1676–1689, the theory was controversial as it seemed to oppose the theory of conservation of quantity of motion advocated by René Descartes. Descartes' quantity of motion was different from momentum, but Newton defined the quantity of motion as the conjunction of the quantity of matter and velocity in Definition II of his Principia. In Definition III, he defined the force that resists a change in motion as the vis inertia of Descartes. His Third Law of Motion is also equivalent to the principle of conservation of momentum. Leibniz accepted the principle of conservation of momentum, but rejected the Cartesian version of it. The difference between these ideas was whether the quantity of motion was simply related to a body's resistance to a change in velocity (vis inertia) or whether a body's amount of force due to its motion (vis viva) was related to the square of its velocity. The theory was eventually absorbed into the modern theory of energy, though the term still survives in the context of celestial mechanics through the vis viva equation. The English equivalent "living force" was also used, for example by George William Hill. The term is due to German Gottfried Wilhelm Leibniz, who was the first to attempt a mathematical formulation from 1676 to 1689. Leibniz noticed that in many mechanical systems (of several masses, mi each with velocity vi) the quantity was conserved. He called this quantity the vis viva or "living force" of the system. The principle represented an accurate statement of the conservation of kinetic energy in elastic collisions that was independent of the conservation of momentum. However, many physicists at the time were unaware of this fact and, instead, were influenced by the prestige of Sir Isaac Newton in England and of René Descartes in France, both of whom advanced the conservation of momentum as a guiding principle.