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The M canique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.

to the English translation of Lagrange's Mecanique Analytique Lagrange's Mecanique Analytique appeared early in 1788 almost exactly one cen tury after the publication of Newton's Principia Mathematica. It marked the culmination of a line of research devoted to recasting Newton's synthetic, geomet ric methods in the analytic style of the Leibnizian calculus. Its sources extended well beyond the physics of central forces set forth in the Principia. Continental au thors such as Jakob Bernoulli, Daniel Bernoulli, Leonhard Euler, Alexis Clairaut and Jean d'Alembert had developed new concepts and...