# A Hundred and One Years of Mechanics

# A Hundred and One Years of Mechanics

Newton to Lagrange via Daniel Bernoulli

*Vis viva* (kinetic energy) was discovered by Leibniz, and ‘s Gravesande’s experiments showed that both momentum and kinetic energy were important measures. The concept of ‘potential energy’ slowly emerged (from the works of Parent, the Bernoullis, Clairaut, and Laplace). Daniel Bernoulli was the first to understand ‘energy’ in a modern way—as kinetic and potential energy, but also as a source of fuel for engines. He managed to calculate the amount of ‘live force’ in air, introducing the formula ‘integral over *P*d*V*’. Maupertuis, Euler, and Lagrange brought in a new idea—the Principle of Least Action, and Lagrange developed a new generalized mechanics using this principle. The Newtonian ‘force approach’ and the Lagrangian ‘energy approach’ are compared and contrasted; and the reason why ‘*T* – *V*’ is as important as ‘*T* + *V*’ is explained. It is shown that Newton missed discovering energy.

*Keywords:*
Leibniz’s vis viva, potential function, hydrodynamica, PdV, Lagrangian mechanics, d’Alembert’s Principle, principle of Least Action, virtual work, absolute motion, force versus energy

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