Sunday, January 25, 2009

January 25: Joseph Louis Lagrange

Joseph-Louis Lagrange
January 25, 1736 – April 10, 1813 

Joseph-Louis, Comte de Lagrange was an Italian-French mathematician and astronomer who made important contributions to classical and celestial mechanics and to number theory as arguably the greatest mathematician of the 18th century.

Before the age of 20 Legrange was professor of geometry at the royal artillery school at Turin. By his mid-twenties he was recognized as one of the greatest living mathematicians because of his papers on wave propagation and the maxima and minima of curves. His greatest work, Mecanique Analytique (Analytical Mechanics) was a mathematical masterpiece and the basis for all later work in this field. It offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century.

He studied the three-body problem for the Earth, Sun, and Moon (1764) and the movement of Jupiter’s satellites (1766), and in 1772 found the special-case solutions to this problem that are now known as Lagrangian points. But above all he impressed on mechanics, having transformed Newtonian mechanics into a branch of analysis, Lagrangian mechanics as it is now called, and exhibited the so-called mechanical "principles" as simple results of the variational calculus.

Lagrange wrote numerous papers on problems in astronomy. Of these the most important are the following:
  • Attempting to solve the three-body problem resulting in the discovery of Lagrangian points, 1772
  • On the attraction of ellipsoids, 1773: this is founded on Maclaurin's work.
  • On the secular equation of the Moon, 1773; also noticeable for the earliest introduction of the idea of the potential. The potential of a body at any point is the sum of the mass of every element of the body when divided by its distance from the point. Lagrange showed that if the potential of a body at an external point were known, the attraction in any direction could be at once found. The theory of the potential was elaborated in a paper sent to Berlin in 1777.
  • On the motion of the nodes of a planet's orbit, 1774.
  • On the stability of the planetary orbits, 1776.

He was elected a Fellow of the Royal Society of Edinburgh in 1790, and a Fellow of the Royal Society in 1791. The Lunar crater Lagrange is named in his honor.

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