The Inverse Variational Problem in Classical Mechanics

The real world is complicated, as a result of which most mathematical models arising from mechanics, physics, chemistry and biology are nonlinear. Based on the efforts of scientists in the 20th century, especially in the last three decades, topological, variational and other methods have developed rapidly in nonlinear analysis, which made direct studies of nonlinear models possible in many cases, and provided global information on nonlinear problems which was not available by the traditional linearization method. This volume reflects that rapid development in many areas of nonlinear analysis Constants of motion; theorem of Henneaux; instructive example of Douglas; construction of the most general autonomous one-particle; Lagrange function in (3+1) space-time dimensions giving rise to rotationally covariant Euler-Lagrange equations; evaluation of the function Gjj; construction of the most general two-particle Lagrange function in (1+1) space-time dimensions giving rise to Euler-Lagrange equations covariant under Galilei transformation; Galilei forminvariance of the Euler-Lagrange equations for two particles in (1+1) space-time dimensions