<P> The fact that kinetic energy is scalar, unlike linear momentum which is a vector, and hence easier to work with did not escape the attention of Gottfried Wilhelm Leibniz . It was Leibniz during 1676--1689 who first attempted a mathematical formulation of the kind of energy which is connected with motion (kinetic energy). Using Huygens' work on collision, Leibniz noticed that in many mechanical systems (of several masses, m each with velocity v), </P> <Dl> <Dd> ∑ i m i v i 2 (\ displaystyle \ sum _ (i) m_ (i) v_ (i) ^ (2)) </Dd> </Dl> <Dd> ∑ i m i v i 2 (\ displaystyle \ sum _ (i) m_ (i) v_ (i) ^ (2)) </Dd> <P> was conserved so long as the masses did not interact . He called this quantity the vis viva or living force of the system . The principle represents an accurate statement of the approximate conservation of kinetic energy in situations where there is no friction . Many physicists at that time, such as Newton, held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum: </P>

When is energy not conserved within a system