Vis viva

Vis viva (from the Latin for "living force") is a historical term used for the first (known) description of what we now call 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 momentum advocated by Sir Isaac Newton and René Descartes. The two theories are now understood to be complementary.

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 term is due to German Gottfried Wilhelm Leibniz, who during 1676–1689 first attempted a mathematical formulation. Leibniz noticed that in many mechanical systems (of several masses, m_i each with velocity v_i) the quantity:

was conserved. He called this quantity the vis viva or "living force" of the system. The principle, it is now realised, represents an accurate statement of the conservation of kinetic energy in elastic collisions, and is 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. Thus the momentum:

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