Mécanique analytique (1788–89) is a two volume French treatise on analytical mechanics, written by Joseph-Louis Lagrange, and published 101 years after Isaac Newton's Philosophiæ Naturalis Principia Mathematica.
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👉 Mécanique analytique in the context of Lagrangian mechanics
In physics, Lagrangian mechanics is an alternate formulation of classical mechanics founded on the d'Alembert principle of virtual work. It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his presentation to the Turin Academy of Science in 1760 culminating in his 1788 grand opus, Mécanique analytique. Lagrange's approach greatly simplifies the analysis of many problems in mechanics, and it had crucial influence on other branches of physics, including relativity and quantum field theory.
Lagrangian mechanics describes a mechanical system as a pair (M, L) consisting of a configuration space M and a smooth function within that space called a Lagrangian. For many systems, L = T − V, where T and V are the kinetic and potential energy of the system, respectively.
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Mécanique analytique in the context of Joseph-Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian and naturalized French mathematician, physicist and astronomer. He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics.
In 1766, on the recommendation of Leonhard Euler and d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, Prussia, where he stayed for over twenty years, producing many volumes of work and winning several prizes of the French Academy of Sciences. Lagrange's treatise on analytical mechanics (Mécanique analytique, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1788–89), which was written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Isaac Newton and formed a basis for the development of mathematical physics in the nineteenth century.
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