Action and Symmetry

Abstract

A small ball rolling in a trough under the action of its own weight is the simplest physical system. The rest state is the simplest history it can have. The ball can rest only at those points of the trough where the tangent is horizontal; otherwise it rolls down an incline. We give the position of the ball by a horizontal coordinate x, and we let V(x) denote its potential energy (proportional to the height of the trough) at the point x. The points x at which the ball can rest are the solutions of the equation dV/dx =0 or dV=0; the increment of the potential energy function as we move a little away from such a point is very small compared to the increment of the coordinate. At these points V is stationary.

“Physics is where Action is.” (Author unknown)