Analytical mechanics ( Fr. Mécanique analytique ) is the work of Lagrange , published in Paris in 1788 , in which he summed up everything that was done in mechanics during the 18th century .
| Analytical mechanics | |
|---|---|
| fr. Mecanique analytique | |
| Author | Joseph Louis Lagrange |
| Genre | scientific literature |
| Original language | French |
| Original published | 1788 |
About work
In the work "Analytical Mechanics" Lagrange completely abandoned the geometric interpretation in mechanics. He reduced the theory of equilibrium and motion to some general equations.
The basis of statics by Lagrange was the principle of possible displacements, and the basis of dynamics was a combination of the principle of possible displacements with the D'Alembert principle . At the same time, he also introduced generalized coordinates, and the equations of motion were rewritten in a new form ( Lagrange equations ).
In this work, Lagrange described the discovery of the second case of the solvability of the problem of the rotation of a rigid body around a fixed point (the Lagrange case). The development of the principle of least action was made by him with its extension to the case of an arbitrary system of points, interconnected and acting on each other in an arbitrary way. The problem of string vibrations in Analytical Mechanics has received a general solution. It was in this work that Lagrange investigated the oscillations of two-dimensional elastic bodies, constructing a theory of the so-called long waves.