TABLE OF CONTENTS KEY FEATURES
The key features of this chapter are generalised coordinates and configuration space, the derivation and use of Lagrange s equations, the Lagrangian, and the connection between symmetry of the Lagrangian and conservation principles.
Lagrange s equations mark a change in direction in our development of mechanics. Building on the work of d Alembert, Lagrange [*] devised a general method for obtaining the equations of motion for a very wide class of mechanical systems. In earlier chapters we have used conservation principles for this purpose, but there is no guarantee that enough conservation principles exist. In contrast, Lagrange s method is completely general and is not restricted to problems soluble by conservation principles. The method is so simple to apply that it is quite possible to solve complex mechanical problems whilst knowing very little about mechanics! However, the supporting theory has its subtleties.
Lagrange s equations also mark the beginning of analytical mechanics in which general principles, such as the connection between symmetry and conservation principles, begin to take over from actual problem solving.
[*] Joseph-Louis Lagrange (Giuseppe Lodovico Lagrangia), (1736 1813). Although Lagrange is often considered to be French, he was in fact born in Turin, Italy and did not move to Paris until 1787. Lagrange had a long career in Turin and Berlin during which time he...
