The Development of Analytical Mechanics by Euler, Lagrange and Hamilton – From a Student’s Point of View

Abstract

The techniques and methods that were devised during the development of ’Analytical Mechanics’ still feature prominently in many branches of Physics, Engineering Sciences and also in various technical applications. In this paper we give an overview of the historical development of this theory by Leonhard Euler (1707-1783), Joseph-Louis Lagrange (1736-1813) and Sir William Rowan Hamilton (1805-1865). The simple example of the pendulum or more correctly the mathematical pendulum serves to illustrate this development. In the conclusion we present a glimpse of the further development this theory has undergone in modern mathematics and physics and discuss some select use cases.