The Golden-Ten equations of motion

Golden Ten is an observation game which is played with a small ball rolling down in a large bowl. This paper describes the motion of the ball in the bowl by means of deterministic mechanical model, which leads to a set of ordinary second-order differential equations. A first impression of the solution is obtained through a numerical approximation, based on some preliminary estimates. Part of the solution is computed exactly, yielding a simple estimation procedure for the coefficient of air friction, which is one of the two main parameters controlling the system (the other parameter is the angle of inclination). An asymptotic solution method eventually leads to an approximate explicit solution, describing the motion of the ball as an elliptical spiral. One of the conclusions is a simple prediction strategy.