Least action principle on an air table

Abstract

In most standard texts, the illustration of the least action principle proceeds through Lagrange’s equations. This approach is severely limited by the mathematical knowledge of the students. We prefer to adopt the experimental approach to mechanics, using air tables; that is, we first study conservation laws, with interactions at a distance as the second stage. We want to show that the least action principle enables both the trajectories and the conservation laws (of energy, momentum, and angular momentum) to be obtained without using Lagrange’s equations.