Introduction to Lagrange.
Joseph Lagrange, whose full name is Joseph-Louis Lagrange, is a famous French mathematician and physicist. 17361was born in Turin, Italy on October 25th and died in Paris on April 30th, 2003. He has made historic contributions in mathematics, mechanics and astronomy, especially in mathematics.
2. Research experience.
During his stay in Berlin, Lagrange completed a lot of important research results, which was the heyday of his life research. Most of the papers were published in the above two publications, and a few were still sent back to Turin.
Among them, the achievements in lunar motion (three-body problem), planetary motion, orbit calculation, two centering problems, fluid mechanics, number theory, equation theory, differential equation, function theory and so on have become groundbreaking or basic research in these fields. In addition, he also made important contributions to some topics in probability theory, cyclic series and mechanics and geometry.
The main contribution of Lagrange:
1, founder of analytical mechanics.
In his book Analytical Mechanics (1788), he absorbed and developed the research results of Euler and D'Alembert, and applied mathematical analysis to solve the mechanical problems of particles and particle systems (including rigid bodies and fluids).
On the basis of summarizing various principles of statics, including the principle of virtual velocity established by him in 1764, he put forward the general principle of analytical statics, that is, the principle of virtual work, and combined it with D'Alembert's principle to obtain the general equation of dynamics.
2. The founder of celestial mechanics.
When establishing the equations of motion of celestial bodies, Lagrange used his principles in analytical mechanics to establish the equations of motion of various celestial bodies.
In particular, according to the arbitrary constant variation method in his differential equation solution, the motion equation with the number of elliptical orbits of celestial bodies as the basic variable is established, which is still called Lagrange planetary motion equation and is widely used.
In the solution of celestial motion equation, Lagrange's great historical contribution is to find five special solutions of three-body motion equation, namely Lagrange translation solution. Two of the solutions are that the three-body always keeps an equilateral triangle in the process of elliptical motion around the center of mass.